In Islam you need the two options : leap of faith and evidences, actually you need the leap of faith before the evidence in most cases, imagine a Muslim in the early ages of Islam heard the Ayya 41 from Surat Ar'rad :
أَوَلَمْ يَرَوْاْ أَنَّا نَأْتِي الأَرْضَ نَنقُصُهَا مِنْ أَطْرَافِهَا وَاللّهُ يَحْكُمُ لاَ مُعَقِّبَ لِحُكْمِهِ وَهُوَ سَرِيعُ الْحِسَابِ
Have they not seen that We set upon the land, reducing it from its borders? And Allah decides; there is no adjuster of His decision. And He is swift in account.
Here Allah give the evidence that the earth ground is not spherical but oval, how could early Muslims accept that ? knowing that this as theory is supposed by Newton in 1689, but no one reject it in the Islam course even if it is not understood yet but they accept it as an evidence from Allah, here a leap of faith is required, then when it was turned into a Fact the Muslims Faith will grow up because the evidence is more comfortable.
In other cases you will find that Allah transacts in Islam with absolute evidences like in Surat al Ghashiyah :
أَفَلَا يَنْظُرُونَ إِلَى الْإِبِلِ كَيْفَ خُلِقَتْ وَإِلَى السَّمَاءِ كَيْفَ رُفِعَتْ وَإِلَى الْجِبَالِ كَيْفَ نُصِبَتْ وَإِلَى الْأَرْضِ كَيْفَ سُطِحَتْ
Then do they not look at the camels - how they are created?, And at the sky - how it is raised?, And at the mountains - how they are erected?, And at the earth - how it is spread out?
These are evidences by the perception of the eye.
The other case you will find Allah make some unknown meaning words, to make Muslims attain the Faith in Al-Ghayb like in Surat Maryam and many Surat where Allah starts with :
Kaf, Ha, Ya, 'Ayn, Sad
This need an absolute Faith in Al-Ghayb (leap of faith) even if the meaning is unknown.
And Allah knows better.