Wiktionary
forge ahead
vb. To move forward quickly, or to make good progress with (especially a plan)
Usage examples of "forge ahead".
There was nothing Captain Turlock could do but forge ahead, hoping that his superior weight and expanse of filled sail would inflict greater damage than he received.
So, Vubben and i hobbled along, urging our hoon, qheuenish, human, and urrish counterparts to forge ahead.
The ship was righting herself as she began to forge ahead and the force of the wind diminished.
But after a while she began to forge ahead of him, sure of her path.