Is the money I lost due to my colleague's actions, and for which I have no documented proof of payment to him, considered a trial (بلاّء), and what should I do about this situation?

In summary: Your colleague committed two forbidden acts. The first is his betrayal of trust, and the second is his lying and denying having taken the money. Both of these are religiously prohibited. As for you, you were negligent by not taking his signature, which makes you liable for the money. However, there is no blame upon you for what happened, as you were mistaken, and this is a trial from Allah, so be patient with it to attain reward.