Few considerations:
F-type stars depending on mass have varying lifespans as main sequence stars. An F6.1V should last for 5.7 Gya.
The planet itself forms physically within 50-100 million years, but the process of the solar system and likely debris clearing would mean 200-300 years of asteroid bombardment which will mean life will not be feasible for a significant period. (Perhaps I am wrong, but did you mean half of the time being spent on setting up conditions for life in this way?)
If you want an Earth-like atmosphere you need a rocky inner core, so something within the frost line. A large moon stabilizes the system and that is likely needed for the proper tidal system in the ocean or even lakes to help generate suitable amino acids in a nuclear geyser. This takes time to set up, but it varies.
More importantly, plate tectonics needs to be functional to fix the otherwise toxic system that comes from natural formation and the bombardment. A large strike which causes the crust to fracture and set the system into motion allows for proper cleansing and the ability for life eventually colonize the whole of the planet.
I cannot see any of these things working within 2 billion years based on purely the process of forming a stable world for which life can actually spread across. Yes, life can exist in niche realms, but if the otherwise whole is too inhospitable then your life will be essentially constrained to volcanic vents and such.
After the primordial crust is subducted and falls into the core you have the proper shielding and the earliest real possibility of a 'mainland' you could use for a map arising. Assuming a lot of things are in line, yes, you could speed up the process of life greatly, but the critical thing your species is a type of crustacean - meaning you need to have suitable evolution to use calcium and phosphorous.
Contrary to <PERSON>'s assertion: " it would not be surprising if evolutionary good luck produced human-like intelligence within two billion years. 801
It is entirely within the realm of realism." is needs to be couched in the fact that practically a billion years of set-up needs to be done to form the planet and get the processes underway for it to work. With stem and crown evolution events being the real driver of natural diversification and evolution through high radiation magma from rifts, the conditions could be possible to speed through a marine environment. Though much of the volatility described would either do almost nothing or possibly wipe out life. Frankly, 1 or 2 cataclysms would be expected.
With your underlying concerns about the planet formation times having been answered, I think it would be easily possible to have your species appear in 2.8-3.2 billion years. Just be mindful that if your planet sits in a precarious spot the natural solar system evolution could kill your planet before it gets the gas giant phase. (Increasing size, heat, luminosity) SO MANY variables here, so I wouldn't go upping to a F1V class to compensate for earlier development of life. (Around 3.6 gya lifespans.)
If you are intent on doing an end-of-times scenario you have plenty of time for life to develop and still be realistic. Hope this helps. 801