We have no idea how long it took the DS to reach Yavin.
There was obviously some time that passed as the Rebels had to study the DS plans to find the flaw. Also, Luke was fitted with a flight suit, helmet and assigned to a group and given a call sign. And I’d like to think he had some time in an x-wing cockpit to see how the controls worked (how to access the targeting computer, locking/unlocking the s-foils, switching from lasers to missiles, ect.) before taking off. So, we know that some time has passed since they arrived. In my head, it was 2 or 3 days. And the DS moves slow.
Yeah. Some time absolutely.
But I dont see why he isnt allowed to sit in his Tatooine clothes?