You simply need to specify your current RE, followed by a letter/number followed by your current RE again:
^[A-Z0-9 _]*[A-Z0-9][A-Z0-9 _]*$
Since you've now stated they're Javascript REs, there's a useful site here where you can test the RE against input data.
If you want lowercase letters as well:
^[A-Za-z0-9 _]*[A-Za-z0-9][A-Za-z0-9 _]*$
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