It does sound like it's a bit big for you, but only a bit. It may not be a problem for you while riding. You can learn to straddle the bike by tipping it to one side or by lifting a leg a bit. This shouldn't be a deal breaker unless it is much too big for you. A snug stand over doesn't tell us enough, so either it's too big for you or it's close enough to the right size.

Is the seat all the way down? That would be a bad sign. When your foot is at the bottom of the pedal stroke, is your foot pointed down, or is it level? Is your knee straight or slightly bent?

Are you leaning very far forward, or is the saddle to handlebar fit comfortable?