Is it too late to pursue PSLF

I graduated in 2016 (started school in 2011). I have been in standard repayment, SAVE, SAVE forbearance, and now PAYE.

I am about to take on a job for the state government, but I am worried that I am too far into my repayment at this point to pursue PSLF. I have never worked for a qualifying employer before, so I feel like it’s too late to start before the tax bomb.

I also worry that given the general instability of government jobs (ie layoffs, budget cuts, departmental downsizing, etc) that it will take me a while to accumulate 120 payments.

Am I too late to start? Is time against me?