Is a crossover needed for TS/SCI from DIA to NAVY? How long is crossover from DIA to NGA?

I am in an awkward situation now. and hope somebody here know what I am facing.
I assigned an offer that need crossover from DIA to NGA. What I heard is 4 weeks waiting time, and I am out of work for almost 2 months already, that means I might need be stay out of work for another month. Now I got another better offer that requires clearance for NAVY. And the company with the new offer promise me to work in 2 weeks, and said I don’t need crossover my clearance since they just need change cage code for my clearance.
I asked my friends about this, and what I got is if I change agency, I need crossover my clearance.
Is a crossover needed for TS/SCI from DIA to NAVY? How long is crossover from DIA to NGA? Is the 4 weeks waiting time max time I have to wait?

Thanks.

There really is no crossover between those agencies, its all DOD. They are just going to get you onboarded into their security process which includes HR and badging stuff, that is what you are really waiting for.

Thanks, @velcroTech .
I found out the reason. The Navy job doesn’t need sci, but NGA one needs.