The purpose of me getting the trademark is to eventually register for an Amazon seller brand. How quickly can this be done?

If you want to join Amazon Brand Registry, you don't need your trademark to be fully registered; a pending status is sufficient. You'll be submitting your trademark application serial number. The approximate timeline to get the number looks like this:

• If you are using the help of an attorney/law firm, you will need to account for the time it takes them to prepare your application. They will likely assess your mark's registrability first. If everything is alright, they will ask you for ownership details, what you are selling/planning to sell, etc. Speaking for Trama, we usually take under 24 hours to assess the trademark free of charge, and then, if the client wants to proceed with us to registration, it takes 3-5 business days to draft the application and get the client's approval.
• When the application is drafted, it will get filed with the intellectual property office. Or, if you are applying yourself, this is the point where you'd fill everything out.
• After the IP office receives your application, it issues the serial number. After that, it usually takes a couple of business days for the number to be recorded in the trademark database and start working.

So, in summary, you can gain access to Amazon Brand Registry relatively quickly, but the speed will also depend on your cooperation or ability to fill everything out yourself. It will also depend on your mark - if there are any issues that might prevent you from registration (i.e. if your mark is too generic and therefore illegible for registration), you'll have to allocate additional time to fix them.

Remember that if your application fails, your Brand Registry access will be revoked. So, although you can gain access a bit sooner, it's advisable not to take matters lightly.