If I have less than 3 cards in my trash, can I still activate Garbage Grabber?

No, you cannot activate Garbage Grabber if you have fewer than 3 cards in your trash.

According to Rule 403.3: "When Recycling is listed as a Cost, the action must be able to be completed for the cost to be paid."

Additionally, as clarified in RiftJudge FAQ #1346 and #3669, recycling 3 cards is a mandatory part of the cost to activate the ability. Because costs must be paid in full to activate an ability, you must have at least 3 cards in your trash to perform the action. If you do not have 3 cards, you cannot pay the cost, and therefore cannot activate the ability.