Corollary: if you want your character to be integrate with the group, then figure out what the typical team positions are for your game and fill a gap.

Tabletop RPGs can be treated like team sports in the sense that they have recognizable positions. Normally there is some sort of front line combat, ranged combat, healer, and stealth combat. People often join a game with a pet character they want to play so if you want to make yourself essential, wait for the other players to declare their characters and then choose whatever character type the party lacks.

This comes with a few caveats: some character types are easier to lay than others. Front line fighting is generally easiest for a newcomer; wizard in D&D and related games is especially tricky. It's fine to start a conversation during character generation and compromise on a balance of utility and difficulty.

Communication skills often get undervalued until after a party has split up. A trivial investment in chalk can write we went thataway on a wall when group members get separated. If you have access to magic skills then your options expand: a minor telepathy ability is invaluable for coordinating tactical combat.

Along the more difficult path of magic use, look for spells that have the potential for multiple purposes. Fireballs are obvious, but a minor telekinesis spell can be nearly as useful in combat situations if you use it to create a distraction by crunching loose leaves before combat begins so the opponents split their forces before combat begins by sending away an exploratory team to investigate the noise. Make full tactical use of partial cover, bottleneck points, and diversions.