I am not going to discuss translating saddhā to faith but how the faith came to humans and what it really is in Buddhism.
There are hundrads of religions in the world.
A particular system of faith and worship can be identified as a religion. Why would someone believe in a religion or a theory?
There are thing that are out of reach to human senses. People needed an explaination to these things because of their thirst to know things (curiosity?).
At the begining they used to believe there is a god or supernatural higher power who can control weather, air water, sunlight, etc. They faced so many troubles due to these things; natural disasters that caused massive distruction heavy loses of their loved ones crops life stock, etc. They they started to believe on a supernatural power who wipes them out for their sins. Thats where they learned so called faith(?).
At those times when humans lived in the forest, it was so common to see their loved ones dying of blood lose. They faught eachother as tribes, were attacked by wild beasts, fell from clifs, blood was not that rare thin to see. Thats where they started to believe it is the blood that has the soul, or the life. Then they atarted to cover bodies with animal blood, animal sacrifices and human sacrifices over their kings or natural disasters.
So called god they believed in was a flesh eater or somehing who demands blood or sacrifices over the good. In reality there was really no god to accept those offerings and make their life better.
Ex: A long before Sri Lanka faced a Tsunami, (as it was recorded we could assume) then they sacrificed a princes to stop the ocean from swallowing the land. After the sacrifice disaster acually stopped. What could have happened? It was to stop no matter they sacrifice the princes or not it was to stop with few waves or may be after the earthquake stopped. They couldn’t just wait.
Similarly when the Nile river floods the people believed it was the god controling. Their polytheism was created based on this.
Most of polytheistic religions have gods who control weather. It is so obious how the god Nun was created.
Nun, also spelled Nu, oldest of the ancient Egyptian gods and father of Re, the sun god. Nun’s name means “primeval waters,”
Some ethnic groups believed in their ancestors, or relatives. They thought theywere in the rivers forests and they are the ones who control these unreachable things. In some cases some of great kings, leaders became god due to their good deeds building or defending their nation.
when we look into EBTs, Paṭhikasutta explains how first thought of a creator (the god) arised.
Now, the being who was reborn there first thinks,
“I am Brahmā, the Great Brahmā, the Undefeated, the Champion, the Universal Seer, the Wielder of Power, the Lord God, the Maker, the Author, the Best, the Begetter, the Controller, the Father of those who have been born and those yet to be born.
(Paṭhikasutta DN 24)
However there are weather controling gods according to buddhism, but they are not the only ones to control it. There are natural facts such as fire element or air element to spread out the clouds and cause drought. An assumption can e made that the water element can increase the number of clouds 
and cause rain. 
(Vassasutta AN 5.197)
Faith to most religions is believing in god or supernatural power, where the definition of religion become something like,
The belief in and worship of a superhuman controlling power, especially a personal God or gods.
However, there is a debate on Buddhism being a religion. In my opinion this is just useless debate where the definition of a religion is not finalized. Some people argue that Buddhism is a philosophy not a religion. I think it depends on the definition of the word “religion”. If that has above meaning Buddhism is not a religion.
But, Sri Lankan cultural definition of the religion is different. A sub commentary on dhammapada says āgama nam buduvajan
(religion means the Buddha’s words). Agama: The word used to name nikayas has meanings such as section, part, dhamma, doctrine, bunch, etc.
Current sinhala word for religion is āgama;
Teachings or a path developed or introdused by a teacher, which consists of a set of advices, rules, rituals, teachings and all related practices. In that sense, Buddhism could be taken as a religion.
Faith is a person’s partner
Saddhā dutiyā purisassa hoti,
SN 1.36
If there is no faith, he would not be able to achieve Nibbāna. Therefore faith should be there. Without faith no one could follow 8 fold path. You are searching for something you o not know.
Lets take a scientist as an example, he has faith on his goal and theories. Without faith could he be able to find what he is looking for?
Mahāsīhanādasutta explains how the bodhisatta went search for what he did not know. He went searching for freedom from the dukkha (suffering). What he did not know was what exactly is the way to find the freedom, what is the freedom.
That is why he practiced a number of different approaches to find the freedom. However, after practicing those for a long time he realized those are not the ways of finding real peace(freedom from all the dukkha).
He achieved all the jhānas tought by Alarakalama and Uddakarāma and realized that is not the real freedom.
And after all these search he left behind two extremes practices aside and started practicing Middle-path. As a result he attained the Buddhahood at Gaya, realizing the Nibbāna is the only thing that has no suffering and one should achieve to get rid of samsara and all the suffering; the four noble thruths.
Then he tought it to his fellows the 5 bhikkus,
Indulgence in sensual pleasures, which is low, crude, ordinary, ignoble, and pointless. And indulgence in self-mortification, which is painful, ignoble, and pointless. Yo cāyaṃ kāmesu kāmasukhallikānuyogo hīno gammo pothujjaniko anariyo anatthasaṃhito, yo cāyaṃ attakilamathānuyogo dukkho anariyo anatthasaṃhito.
The Middle path:
It is simply this noble eightfold path, that is:Ayameva ariyo aṭṭhaṅgiko maggo, seyyathidaṃ—right view, right thought, right speech, right action, right livelihood, right effort, right mindfulness, and right immersion. sammādiṭṭhi sammāsaṅkappo sammāvācā sammākammanto sammāājīvo sammāvāyāmo sammāsati sammāsamādhi SN 56.11.
Reading bodhisatta’s story we can see it was the suffering that motivated the bodisatta to go search for the freedom. The buddha said the same in Upanisa Sutta
The sutta explains the vital facts that are in need to achieve nibbāna. The same thing is explained in Kītāgiri sutta where the buddha states the fact that one should have the faith to come into the path.
It’s when someone in whom faith has arisen approaches a teacher. They pay homage, lend an ear, hear the teachings, remember the teachings, reflect on their meaning, and accept them after consideration. Then enthusiasm springs up; they make an effort, weigh up, and persevere. Persevering, they directly realize the ultimate truth, and see it with penetrating wisdom MN 70.
From the story of bodhisatta we can see what motivated the bodhisatta to go search for freedom (Nibbāna ). It was the sufferings which led him to Nibbāna.
Rebirth is a vital condition for suffering
jātūpanisaṃ dukkhaṃ,
Suffering is a vital condition for faith.
dukkhūpanisā saddhā Upanisa Sutta.
We suffer because we were born into this world. So there must be a way to get rid of all the suffering.
When we look at religions in the world therr are very less number of them that offer a chance to free will. When we believe in god who created us, (sometimes to hate him, not to believe) there is no chance to end all the suffering. And what if there is no rebirth and transmigration (samsara). Why would we suffer finding the freedom?
There are scientifically proven stories about rebirth.
Ex: Ian Stevenson’s reasearch.
So we should find a way out of this mess. Who are the ones to offer us a way out. Believing in god would help? I do not think so.
Buddhism offers you a path to get rid of all the suffering where you have a chance to change yourself on your own. Achieve nibbāna on your own. There is no chance for a god (creator) in Buddhism.
Tumhehi kiccamātappaṃ, akkhātāro tathāgatā;
Paṭipannā pamokkhanti, jhāyino mārabandhanā. SN 12.23
You yourselves must strive; the Buddhas only point the way. Those meditative ones who tread the path are released from the bonds of Mara.
The Buddha show us the path, going along and achieving is up to us. Isn’t this enough to have faith on the Buddhism.
Whatever the suffering explained in Buddhism is all there, just close your eyes for a moment think of your life how many times you have suffered even right now your body pain that you try to hide by changing your posture. Suffering of loosing someone you love, from diseases, disorders, etc. It all explained in buddhism how they arise how to get rid of them (the four noble thruths).
The experiences explained about the path bojjangas, jhānas fruits and nibbāna, you could see in this very life. One attempt to see them before you die would never go waste.
That is why I am here, I beleive in the Buddha and the path he explained.
When you say you mean it:
Buddhaṃ saraṇaṃ gacchāmi
by knowing there is no other teacher in this world to teach the eight fold path to Nibbāna.
Dhammaṃ saraṇaṃ gacchāmi,
by knowing it is the dhamma where we can find the word that lead us to Nibbāna.
Saṃghaṃ saraṇaṃ gacchāmi.
by knowing only people who achieved the Nibbāna, following the path is them. Either the Buddha or real his pupils can teach us the path, (even existing samga) and be good friends (kalyānamitta).
Normally I do not write much, there may be typos, errors etc.
