Can you play Abandon without having to counter a spell?

No, you cannot play Abandon without a valid spell on the chain to target.

According to RiftJudge FAQ #5039 and Rule 4070, if a spell requires a target, you must have a legal target available on the chain to put the spell on the chain in the first place. Since Abandon specifically says "Counter a spell," it requires a spell on the chain as a target. If there are no spells on the chain, there is no valid target, and you cannot play the card.