If Explorer's Cache isn't on the battlefield as its activated ability resolves, you can't remove a +1/+1 counter from it, so you won't put a +1/+1 counter on the target creature.
This artifact enters with two +1/+1 counters on it.
Whenever a creature you control with a +1/+1 counter on it dies, put a +1/+1 counter on this artifact.
: Move a +1/+1 counter from this artifact onto target creature. Activate only as a sorcery.
To move a counter from one permanent to another, the counter is removed from the first permanent and put on the second. Any abilities that care about a counter being removed from or put onto a permanent will apply.
: Move a +1/+1 counter from this artifact onto target creature. Activate only as a sorcery.