Even Philosophers make a leap of faith. In fact, they make many.
Believe in yourself and go forth
I take the above from the entrance to Victory Road, the long cavern I had to traverse in Pokemon Ruby. I was somewhere between 5 and 8 years old when I played it first I think.
Philosophers take a leaf out of Pokemon Ruby. They make a whole host of Philosophical assumptions before they can even begin Philosophising - one of which is beliefs such as that you exist! After all, if you denied yours and others' existence when you started Philosophising, what sense would it make to build rational arguments on the basis that you had understood the last step? I rely on my verification
Faith is something of a dirty work in 'rational discourse', largely because the rationalism of the Enlightenment has been so 'successful', that it has made anything which looks in opposition to these ideas a no-go zone.
Where to begin
Philosophers have to begin Philosophising somewhere, and when they do, they necessarily make assumptions about Philosophising being worthwhile in some way - it is only by Philosophising, after all, that we even deduce that Philosophy might be worthwhile! It clearly isn't immediately obvious that Philosophising is worthwhile (do people choose to philosophise or play video games/ watch movies/ go to the pub/ play sports/ literally anything else on a Saturday evening?)
It's a complex issue
Oh, and what if issues are infinitely complex?
We assume, that by Philosophising, we might reach 'the truth' (or at least most do).
This is an enormous leap of faith that:
a) Philosophical methods could achieve such a thing (and that such a thing exists!?)
b) That the questions have 'solutions' of 'limited complexity' (i.e. with our finite reasoning and steps we can reach an answer)
And on that bombshell...
Good luck to those of you who want to Philosophise. And to those of you who don't... fair enough I guess!