Maybe some cars turn over slower. I don't know, never been around a Suzuki. All's well that ends well. You can never go wrong cleaning terminals. A lot of current is flowing when starting. I guess you know that one can weld with stick arc for a minute using a 12v battery.

Out of curiosity I measured the output voltage of a red-top AGM while starting a four cylinder turbo car that was sitting for six months.

The minimum voltage was just below 11 volts.

Regulator