If you ever read the plot of any Metroid game, you would notice that they never continue right after a game (i.e. Samus destroys Motherbrain and happily tells her Commanding officer, then gets shipped to SR388). Your beginning sounds a little to… happy and cliche’d. It would be better of to omit the part where she happily reports to her commanding officer and just get to the part about the time machine.
The plot is just a little cheezy and unmetroid. A time machine?
“Samus returns to federation federation flagship to give the Omega cannon to secure hands, and receive her reward.”~Something like that.
But the part about the time machine sounds bad. Samus just goes there, and it happens to be a time machine? I doubt they’d ask her to go to a time machine just like that, even if they wanted her to protect it.
The engine is fine, but you might want to rethink the plot a little.
The part about continuing right after Hunters is perfectly fine, as Super Metroid takes place right away after Metroid II.
A “time machine” sounds like it could be interesting as long as it’s pretty limited technology. As in, it can only speed up or reverse time for someone, or (since that’s kind of cliche) something similar. You could work that into the game by having pirate experiments using that technology and giving Samus a “time suit” of some sorts or something. Just try to avoid making it too complicated and open for plot holes… because time machines can easily rip apart a plot. They might make for cool puzzles, though.
You also have to come up with a reason for the GF telling Samus of the time machine technology, other than “help us protect it in case there’s an attack or something lol oh noez here it comes”. Also be sure to come up with something better than the only solution I can come up with at the moment. (“warnings from the future” )