Can you tell me how long it should take to overcome hypersomnia caused my depression and medication?

That depends: If you have hypersomnia due to depression, than it may not resolve until your medications are finely tweaked (optimized for you). On the other hand if you have been on a medication that is causing sedation or hypersomnia that is not resolving - that merits exploration with your prescribing provider.

Hypersomnia: If good response from depression treatment usually 3 to 4 weeks, same for medication, you may build tolerance to the sedating side effects in 3 to 4 weeks usually.