There is no "process" until Pelosi calls for a formal proclamation (vote) in the House authorizing the impeachment proceedings. No representative, not even the Speaker, can just decide to impeach anybody. Once the vote is taken, Pelosi owns it and has to see it through to any conclusion. By announcing the "impeachment inquiry" without the vote, she can step back once it blows up in her face(and it will). She's trying to have it both ways. In other words- more politics.
Trying to have it both ways is human nature; it's why we have to teach kids they can't eat all their cake and still have any. Some kids grow up, and may even become President, without ever learning that.
That's why the pretend adult in the Oval Office can cheat people by claiming to be broke but boast that it made him billions, so he must be smart. Pelosi's just playing the political version of his game. If the evidence that comes out is as bad as Donny's fearful obstruction signal it is it is, it may well be enough to convict him in the popular vote, even if his toadies in the Senate can't find the gonads to do it first. And it was the Squad's idea, not hers.
Anyway, even if there isn't the evidence to get a Bill of Impeachment out of the House, Donny's behaviour and what proof there is won't win him any new votes. More likely they'll cost him some soft ones. At the same time, and more to her needs, it'll calm the waters within her own Party, and get them back on a more useful course.
With the preview that Mueller testimony gave us, it's clear Donny can't/won't come clean. His only 'defence' is: Not proven; no matter how incompetent, nasty, wrongful, unethical, immoral my actions have been, I have kept any evidence secret, so there's still reasonable doubt they are high crimes or misdemeanours.
That won't improve his electoral prospects any more than the 'achievements' — which the people clearly do not value, as he tweets about them to so little effect — that have left his minority support stalled in the 40's. Where it began. Before anyone knew what kind of of a President he'd be.
That's how democracy works, the final word that we trust always comes from the court of public opinion.
If people had the same faith in confections like electoral colleges, or impeachment inquiries, we wouldn't need votes at all.