yeah, that's the only real downside when using massedcompute - there is no storage function (yet).
I don't know if they will implement it but it has been suggested many times as far as I know.
so far, if you really want to have a storage function, you have to use runpod.
For me personally, I tested both a lot and sticked with massedcompute.
Cheaper and much faster, even though you do the installations again every time..
If you use a good file system like google drive (you can log in from the rented machine and download), the file downloads don't consume much time anymore
loading the image and making the installations though.. that takes a little time.. you cannot avoid it unfortunately
suggestion: try to work in time-blocks. several hours at once for one session if possible.
And be wise to which GPUs you rent and for what.
A6000 ist very cheap but has limited storage.
L40s and A100 are a little bit more expensive, but very nice to work with as you have a lot of RAM and storage, but keeping them running over many hours get costly quickly.
hope that helps