enter upon
come upon
luck into

And here we enter upon the most difficult of all our problems.

He would run away from home and enter upon it.

In about 1560 he entered upon the work with which his name is associated.

We may be entering upon the first true peace the human race has ever known.

Nor could I simply enter the house upon my own initiative.

What are the odds of entering a man upon one, two, three, four, or five points?

All seemed weary of life even before entering upon it.

I have no way to enter upon the pathways of power and influence.

However, at the end of the 14th century it entered upon a steady decline.

And yes, now that you mention it, there is someone special entering upon the stage.