You can definitely use it for a forward.
You would need to remove the gap, though. Otherwise, the low magnetizing inductance will produce too high a magnetizing current. For a forward, the magnetizing current does nothing, just wasted power, because it adds to the actual secondary reflected current, so the primary and the transistor have to conduct this current, leading to high losses.
Depending on how the transformer was built, the air gap can be with shims in the outer legs, which are easy to remove, or it can have the center leg ground down. Removing that kind of air gap is not easy. It can only be done by grinding down the outer lesgs of the affected half. That can be done even with fine sandpaper, but it is extremeely messy (dusty) and you have to make sure they are flat. It can be done with diamond-coated tools, similar to the ones used to grind down the center leg at the factory. But it is unlikely you will have access to such a machine.
If you have two of these transformers, then you can build up one, using just the unaffected core halves.