There is no way to rule out all potential threats, but:
Lufthansa, Germanwings’ parent company, is widely seen as having one of the best recruitment screening programmes in the industry, carrying out in-depth interviews and psychological testing before candidates can begin its two-year pilot training programme and filtering out more than 90% of initial applicants.
While it, too, has no formal psychological testing programme once pilots have qualified, the company has a generally effective self-monitoring and reporting system. This actively encourages pilots who experience potential problems themselves or observe them in their colleagues to report them to the airline without fear of repercussion. No such report was filed in relation to Lubitz.
Any assumption that periodic psych screenings after hiring would prevent extremely rare incidents like the Germanwings crash would be misplaced. Moreover, the kind of depth eval that might possibly be a bit helpful would probably run afoul of employment law in the US. Too intrusive and far too many false positives to root out the needle in the haystack.
Best bet, IMO, is non-retaliatory coworker reporting, self-reporting, and two crew in the cockpit rule.