I just capped a new character yesterday, spending a few hours just doing that, getting from 109 to 110. Popped an AK20 tome, and within the same day, got to AP level 20. Not even properly grinding it, that was just from dungeons and WQs and other side stuff I did along the way of the gear grind which I actually made less progress on (this character is still below 810, so I didn't even have access to heroics yet)
I suspect getting to 35 will not take very long at all, in fact by being bestowed with instant AK20 upon level capping, just doing Suramar probably gets it most/all of the way there, if not overshooting, especially if one waits a few days for it to pool up to AK25.
The gear grind also doesn't feel like it takes terribly long imo. If you're rerolling for heroic NH, yeah that'll take a while, but from the last alt I did, even before 7.1.5 it only took a few weeks to get to ~865ish, WITHOUT dumping tons of gold on the character to give them all kinds of crafted gear.
All in all the most painful part of rolling a new character to me is actually the exp grind from 1 to 110 (or 55 to 110, even) more than anything else. Which is crazy considering all the heirlooms and exp pots and other things you can abuse for efficiency. There's no weekly lockouts or time gates on exp.