Your Honor progress depends largely on your own behavior. If you feel like you're making no progress whatsoever, then maybe you're still being negative enough to hold yourself back. It's not enough to just not get punished to progress in Honor - valid reports against you, even if they don't result in a punishment can slow or halt your progress.
Also, getting Honored from players in your own premade has no effect whatsoever, which means that, if you're trying to cheese Honor gain by playing with friends to get guaranteed honors, you're not actually being Honorable, and aren't getting anywhere to boot.
From the Honor FAQ:
Can I game the system and boost to level 5 by constantly playing with a premade and honoring each other every game?
Nice idea. We had it too. So we specifically built Honor so potential exploits like this give you (and your friend) literally no benefit.
If you want to gain Honor, get yourself out there and be honorable with randoms. At the very least, get the Team Honor bonus, and at most, work to get Honors from your teammates.
And, lastly, to address "how long until Honor Level 1" - there's no set-in-stone time for it, but going up in Honor is meant to be a long-term progression. To give an example, let's use my own Honor progress:
I started out the year (Jan. 8th, I think?) at Honor Level 2, Checkpoint 3, since I made it to Honor 5 in 2017. I couldn't guess as to how many reports I got over the course of these past four months, much less how many (if any) were valid, but, two days ago, on 4/13, I hit Honor Level 3, Checkpoint 3. Essentially four months of consistent play and (largely) sportsmanlike behavior led to me going up (more or less) a full Honor Level. 'Course, I'm not Honor 4 yet, but, still, math.
So, TL;DR
- Do more than just not get punished, and certainly do more than just be neutral. Be positive.
- Don't try to get Honors through premade teams you make, 'cause that doesn't work.
- Honor others - because, if nothing else, you'll contribute to the Team Honor bonus, and that benefits everyone.
- Don't expect immediate progress. It is a year-long ordeal, after all.