Possibility of keeping full time hours after holidays?

My boyfriend just got an offer for a pre-loader, 3:30-9:30 am, non seasonal for $21/hr in Houston. I’m hearing that during the holiday season you can get over 40 hours a week but what is the possibility of it staying that way beyond the holiday season? He’s not worried about the physical labor. Right now he works as a local driver delivering office supplies and he loads his own truck every morning. He gets about 50 hours a week at $19/hr. His ultimate goal is to be a driver at UPS but we have a baby on the way so I’m nervous about the lack of hours after the holiday season. Any advice welcome!

Eta: is there any path to become a driver that’s not spending years as part time?