You start Borderlands 3 with a very limited inventory space, and your backpack can only hold a total of 15 different items in the beginning. This space is quickly filled up when you do missions, so it's smart to upgrade your inventory space early on to allow you to bring back a lot of loot from your exploration.
Luckily for us, we are able to upgrade our inventory space very early on in the game. You can upgrade it after having unlocked your ship after finishing the mission on Pandora. Most players will be around level 6 to 8 at this time.
Anyway, head to Markus' space in the ship and look for a large screen that sells SDUs there. Find the one with backpack space increase and buy it. Each SDU cost cash, and most players will be able to afford the first upgrade by the time they are on the ship for the first time. Each SDU add 3 new inventory spaces that are permanently yours to keep, but each new SDU also get a bit more expensive than the previous one, so you can't buy many right away. However, keep saving cash and you can buy a new Inventory Space SDU every once in a while.