That's why most players opt for ...e6 at the start rather than ...e5. Also conventional wisdom is that giving up your queen for two checks (let alone queen AND rook) is a bad idea, unless perhaps your opponent's king is quite exposed and a third check looks fairly imminent.
This topic came up some months ago, and I gave some statistics which suggested White's advantage might be roughly similar to the advantage in standard chess. Have a look at https://www.chess.com/forum/view/chess-variants/does-white-have-too-much-advantage-in-3-check
Also here are some useful general tips: https://www.chess.com/blog/GM_Kenny_Ji/3-check-chess-tips
1. three is a small number
2. an attack strategy i figured out is to check my opponent and then follow it with a second check where my opponent only has 1 life and i will most likely win because i just have to give check even if i'm down a queen and a rook and probably even more
3. f7 and f2 are even weaker than in standard chess because 1.e4 gives the queen and bishop access h5 and c4 that both can easily attack f7
3. i learned that it is good to bring the queen and bishops out early because they can both check on f7 or f2 to bring my opponent down to 1 life
4. white has the first move and therefor has a head start in bringing the queen out early
5. here's an example