You are very correct, yes, 250 is more than enough! A menu can be accessed (by pressing left tab) that allows you to purchase upgrades, purchase vehicles for automation (this will come in handy later, for now most of your box collection and depositing will happen manually), view tutorials and save your progress. Through purchasing upgrades, your 250 boxes should allow you more than enough points to upgrade climbing, jumping and other stats, through which you should be able to escape not only the room, but potentially even the cave as well!