Without knowing a lot about how much time you have to put into this, I’d say writing your own engine for The Awesomest Game Ever and have it in a polished state

Without knowing a lot about how much time you have to put into this, I’d say writing your own engine for The Awesomest Game Ever and have it in a polished state for a summer release seems like you’re asking a lot from yourself. Find out what you really want to build and find out what you can ditch or reuse so you can spend more time on what you’d actually enjoy doing. If you want to build a game engine, consider scoping your game so you spend more time on writing the engine and less on story, mechanics, balancing, etc. On the other hand if you just want to worry about the player’s experience then I’d suggest using an existing engine. But you can also decide to extend the deadline and go crazy on building on your own engine with the kind of gameplay and lore you’d want.