The Government Accountability Office (GAO) issues a decision on a bid protest within 100 days after it is filed. There is also an express option which shortens the decision timeframe to 65 days. The agency is right that the process takes time. For federal contracts, the process follows FAR Part 33.104 and the GAO's own regulations. This is different from state or local government bids, where the timeframe for a protest decision would depend on that specific state's procurement code and the rules of their vendor portal.
My firm mostly works county and school contracts, but we have done a federal building. We've seen protests slow things down. When a protest is filed, the contracting officer must suspend performance of the awarded contract if the agency receives notice from the GAO within 10 days after contract award, or within 5 days after a required debriefing. This automatic stay means the awarded contractor cannot start work until the protest is resolved, unless the head of the contracting activity makes a written finding that it's in the government's best interest or there's an urgency.