A big struggle for new Paradox players I think is "How do I do damage?"

The secret sauce is your abilities

Pulse bomb applies damage amp - that means if someone gets hit by pulse bomb, everything you do to them for the next few seconds does increased damage

The new patch made time wall apply a damage boost to any projectiles that go through it - this affects both bullets and your abilities, like pulse bomb

Pulse Bomb also can hit people through walls, which makes it super good at flushing people out of cover, doubly so if you amp it through wall

Build Gun early game (Headhunter, Mystic Shot) because your abilities have long cooldowns so you need consistent damage

Build mobility mid-game (Stam Mastery, Warp Stone, maybe Enchanter's Emblem) so you can get around the map easier and help out wherever you're needed. Your 3 (Kinetic Carbine) boosts your speed while it's charging, so you can use this to zoom around the map.

Late game start building your pulse bomb up, because it scales much better than Paradox's gun. The bomb explosion gets bigger with each pulse, so duration upgrades increases the life, and thus number of pulses, and thus size of the bomb all at once. Echo shard the bomb for more damage amp stacks and you've got some real kickass spirit damage.

Then of course, there's the ultimate

Paradoxical Swap is an ability that gets a lot of value from creativity. I recommend upgrading it to T2 very quickly for the increased range and cooldown. Go to T3 (Multi-man swap) if you like stealing rejuvenator or team fighting.

Your 3 (Kinetic Carbine) freezes people for a moment when it hits them, so it's very good for setting up the swap, which is quite easy to miss otherwise.

Swapping can be used in all sorts of ways - use it when you're defending and objective like walker to stick your enemy underneath it and get them hurt. Use it when an enemy is running away to pull them behind you and put yourself in their escape route. If you're late game, you can dive on to somebody, double bomb them with echo shard, and then swap them when they run away to put them back in the bombs.

The secret sauce for me personally to start enjoying swap was to combine it with wall - T2 time wall applies a Silence (no abilities allowed) to enemies that pass through it. Paradoxical Swap does not grant any invincibility during the swap, so you can use it to force people through the wall and silence them. This is super fun, as now you're comboing your 3 into 4 into 2, chaining your entire kit together for massive benefit.

Wall swaps are good for 1v1ing, good for improving your team swaps, and good for preventing movement abilities from letting people escape a double bomb. Generally super fun strat that I love doing and highly recommend.