Nope, you’re stuck starting with 8 scouts, 2 vipers, every single time.
The Gambits expansions do give you a couple of extra starting cards that either allow some extra actions whenever you choose to scrap them (like draw two cards, or gain two trade) or some permanent upgrades throughout the game (gain 1 attack at the start of each turn, vipers have +2 attack). That’s as close as you’ll get to a unique starting deck in Star Realms.
The only other set that changes the goal significantly is the Missions expansion, which gives you an alternate win condition–finish your 3 unique missions. You can still win the standard way, but the missions give you something else to shoot for if you can’t put together a good deck.