It's possible, but...
RTX 2060 Super > RTX 3080
That's 700-800USD gone already. 2nd hand 2080Ti may be an alternative, if you're ok with that.
550 Watt PSU
No specs on this at all, but I'm going to assume that needs to go too.
A nice 750 Corsair RMX ought to do, but you might be able to get away with less, like the 650w model. The recommendations are generally exaggerated to account for all the varieties of system configurations.
Anyways, that's ~140USD gone.
It could end there, but there's another potential issue: the i5-9400F.
If you play, or start playing, titles that can utilize more than the 6 threads it has, then a sustainable 60fps may not be possible without adjusting or turning down some settings in order to get around that limitation.
A new cpu will definitely take you over the 1000USD limit:
-possible upgrades are 9700(plus variants) and 9900(plus variants).
-your current cpu cooler may not be adequate for any of them.
-if you look to the 9900(plus variants), these things really can't be run on any cheap motherboards - Z390 and Z370 only.
If you're fine with changing some settings here and there for more cpu thread heavy titles, upgrades within 1000USD is definitely possible.