The Dilithium Mine is live.
I would suggest Priorities like this now:
Upgrade Industrial Fabricator (this will slightly reduce the Dilithium Provision costs)
Then level and upgrade the mine at least to Tier 1
Then upgrade the rest of the main base to benefit from the first dilithium mine discounts.
Basic leveling should remain mainly on the mine in the meantime until it is done.
After that back to the Embassy.