This specific instance was when he was flying to Namek right after beating Vegeta for the first time at the beginning of DBZ. Where he needed to go outside the ship while it was in transit. He’d never been to space and had no reason to think he’d be fine without a suit

By the beginning of Dragon Ball Super he does go into space to fight Beerus, but he’s not there for long. It seems he can go in space for a bit, but needs to come back to breathe. This also tracks because he’s had to learn to control his breathing in multiple different ways