High Crimes and Misdemeanors

     This is the long answer to whether an impeachable offense can occur prior to one's being elected or appointed to a federal office. There is no doubt that those offenses can be investigated. The Bill Clinton investigations are the obvious precedent. However, there has also been precedent for impeaching a federal official for "High Crimes and Misdemeanors" that occurred before the official took office.
     The following is from the Congressional Research Service, which is the public policy research arm of Congress. The report was prepared in 2015. It generally discussed impeachment, and it particularly discussed our question.

Impeachment for Behavior Prior to Assuming Office

Most impeachments have concerned behavior occurring while an individual is in a federal office. However, some have addressed, at least in part, conduct before individuals assumed their positions.

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Judge G. Thomas Porteous, in contrast, is the first individual to be impeached by the House and convicted by the Senate based in part upon conduct occurring before he began his tenure in federal office. Articles I and II each alleged misconduct beginning while he was a state court judge as well as misconduct while he was a federal judge. Article IV alleged that Judge Porteous made false statements to the Senate and FBI in connection with his nomination and confirmation to the U.S. District Court for the Eastern District of Louisiana. On December 8, 2010, he was convicted on all four articles, removed from office, and disqualified from holding future federal offices.

     As you can see, there is precedent for not only including prior offenses in articles of impeachment, but in finding the defendant guilty. Besides this precedent, there are also the words of Alexander Hamilton, who described impeachable offenses as relating "chiefly to injuries done immediately to the society itself." Stealing from a Charity is injurious to society itself.
     Remember, the House of Representatives is not limited to issuing articles of impeachment based only on the report of Special Counsel Robert Mueller. They can expand the charges as they see fit.