I don’t know how weapon solicitations work, but I bid on multi-million dollar US Government contracts for synthetic jet engine oils for 20 years and found the people and procedures to be absolutely fair and unbiased, that is they faithfully followed the rules. As for the rules being fair and unbiased, that is a different story.
The only protest I ever saw was one that I filed when a large oil company conspired with a small business to win the small business set-aside portion of a contract. The small business then conspired with a "disadvantaged" business to get a 10% bid advantage. Since the definition of a disadvantaged business hinged on the country where the owner was born, I filed based on the fact that the product was actually manufactured by a large business, and the disadvantaged business criteria was discriminatory.
The DLA investigated and ruled against me on the grounds that the rules were followed, even though the rules were flawed, so I appealed to the GAO. They agreed with the DLA, so I filed suit in Federal court. The judge bit on the discrimination aspect and, being an election year, the DOJ immediately wanted to settle. Net result is I was awarded the contract, the competitor was disqualified, and the rules for disadvantaged businesses were changed.
So such challenges can be won if they are legitimate. If Glock has material grounds based on procedures or bias they may have a bona-fide case, although they may have to bump it outside of the military system. If it is just sour grapes it will be disposed of in fairly short order.