Here's how to check if your cranks & pedals are centered on the bike:

Turn the cranks until the left crank points up along the seat tube. Measure from the left side of the seat tube to any convenient distinct point on the left pedal. Now turn the cranks 180 degrees so the right crank points up. Measure from the right side of the seat tube to the corresponding point on the right pedal. Your two measurements should be identical.

Sometimes (especially on cheaper bikes) the manufacturer won't match the bottom bracket to the cranks. They'll use whatever bottom bracket they can get cheaply - even if the pedals aren't symmetrically located.

Having a gap between the crank and frame is common. There might be a similar gap on the right side - but you can't see it because the chainring and its mounting spider block the view.