I have a 100 AMP Pushmatic breaker box in my garage. It is full of breakers that are all 120 volt that ranger from 15 to 30 amp. I want to hook up a 240 amp for a pump motor and a one for a welder. Can I hook up two of the 30 amp 120 volt breaker to accomplish this with each one?

As a temporary measure sure, but should not leave it as is indefinitely, as if there is a short or overload, only one pole will trip leaving the other pole on. Or worse if someone uses the breaker as a disconnect and mistakenly only shuts one pole off.

ITE Bullgog PushMatic breakers are still available, hard to find but they are out there.

These panels are a bit unique in that one leg is one entire side, and the other leg is the other side. If you have any 2 pole breakers you can see the each pole sits across the bars to connect to each leg to derive 240 volts.