They did have solid evidence to impeach Trump. He's been impeached.
Impeachment is a tricky matter because the articles of impeachment did not cite a particular crime that Trump committed which takes away from the objectivity of the charges. A President can be impeached for essentially anything so to say there was evidence of impeachable related offenses is technically correct but does not set a good precedent because you could make this argument and cite evidence for impeachable offenses in every single Presidency in American history.
Looking at the timeline of events, near August Democrats were accusing Trump of bribery related charges by tying military aid into investigations with Joe and Hunter Biden. Was it wrong of Trump to ask for investigations into his political opponents? Sure. I'll concede that point because it isn't a good look for the President of the U.S. to be inquiring about his political opponents via proxy of a foreign country -- Have the U.S. Department of Justice handle it. But, there was not enough evidence to suggest that Trump had sought out investigations into Joe Biden and Hunter Biden with predication of those investigations being linked to the release of military aid. Democrats knew they could not charge Trump under the legal codes of extortion or bribery so they chose broad charges of Obstruction of Congress, which he has the legal authority to do, and Abuse of Power which is too subjective of a charge.
When Nancy Pelosi was asked about this,
she didn't have an answer stating that it was up to the lawyers she worked with to cite the specific charges. Keep in mind, a month prior to this statement, she was on the record stating that Trump would possibly be charged with
bribery related charges. Regardless of your views of Trump, this was not a good move to impeach. Public support for were pretty much across party lines shown by polling data with independents split on impeachment. There's an election coming up in 2020, support for Trump should have been decided there. Combine this with Nancy Pelosi holding impeachment charges in the House, I can't help but believe this is partisanship taken too far.
Impeachment requires "high crimes and misdemeanors". The articles votes on don't seem to include any statutory crimes making them invalid. Furthermore the articles of impeachment have not been submitted to The Senate, meaning technically until that has been done, the legal prerequisites for an impeachment to be valid have not been completed.