AU accounts only but decent score, denied car loan - how to proceed?

[Anonymous]

 As I recently immigrated from Canada, I only have AU accounts from my wife's accounts in good standings (4.5 years of history, 45K of CL w 1% utilization, 5 accounts - which equal out to a 766-788 credit score).  However, we recently were looking at getting a car loan and were denied because of my "thin file".  We are also considering buying a house in the next year.

  Thinking of getting some credit cards myself to help this (maybe even a credit building loan?), but super concerned it will tank my score with it dramatically lowering my age of account and the new accounts opened.

  I know that the car loan / mortgage lenders use different scoring methods, what is the best way to proceed here?  Really appreciate any thoughts/advice!

[Revelate]

If you're looking to buy a house in over a year it may be worthwhile to open up a single credit card now.

That said, there are plenty of lenders that will underwrite on even a single AU tradeline currently, and that new account will be a penalty for longer than a year anyway under the EQ and TU mortgage scores (don't know how long that lasts I just know my own report complains about them even after FICO 2/8/9 dropped that reason code completely at the one year mark).

I'd look at what my mortgage scores were before I did anything TBH.