I think you should be more than fine as long as you keep up with the challenges. The season lasts for 90 days, and today is the halfway point with 45 days left. I finished a couple of days ago so even if you started today it would've been possible to complete it.
Progression stays the same once you reach level 20. From that point it's always 660 fame to reach the next level:
https://fallguysultimateknockout.fandom.com/wiki/Season_1
By my calculations you have ~46,000 fame needed to complete the pass. The weekly challenges vary in difficulty but I think most people will be able to get 4,600 fame from it relatively easily. There's about 6 weeks left, so that's 27,600 fame from easy weeklies. That leaves you with 18,400 fame that you'll need to get from dailies (720 fame per day) and from just playing the game. With the dailies, it would take you 25 days to get the rest. It'll be even faster if you can do the harder weeklies.
Also, near the end of the season there's supposed to be a fame boost event that'll reward x2, x3, or possibly even x4 fame.