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Theoretically, sure. If you can find a GS-12 position, step 1 is at $86k.
That said, there are several caveats:
1) Unless you can get your current client to write a PD specifically for you or use some sort of direct hiring authority, breaking into the feds is a long shot if you're not a vet or don't have a disability.
2) At 4 YOE, there are a TON of people applying for GS-12 and GS-13 positions in the DC area on public announcements; presuming that's where you're applying, the competition is very stiff and you're likely to be passed over for someone with more years of relevant experience even if you manage to not get blocked by folks with vets pref
3) You'd likely have a better shot at applying for a GS-9 or GS-11 position, aforementioned vets/disability preferences aside, but you'd take a pay cut as a 9 even if they gave you a step 10 (which isn't at all a guarantee) and would need to get a starting step of 6 or 7 as an 11 to be in the same salary bracket, again with absolutely no guarantee of receiving a higher starting step.
I was a fed HM at two civilian agencies, happy to answer any questions you might have.