You will need to be patient.
It took a few days for me, then I was rejected initially because I hadn’t filled out satisfactorily the ‘why I want to be a developer’ question. Even though the question was labeled optional. So I guess the 1-2 weeks they state in the email you receive after the application is fairly accurate, maybe longer if the processing team is on holiday.
The legalese distributed with the SDK is clear that Trimble is concerned about random developers creating malicious code - perhaps a competitor wanting to slow down Sketchup so people stop using it, etc. So I understand why they want to vet each request so thoroughly.
But really, the API is free via Ruby script - although substantially slower it seems. I’m looking at speeding up my importer by rewriting it to us the SDK, but I will need to learn how to use C first.