Luke 1:26 God sent Gabriel. GOD SENT! Gabriel was but the messenger.
Luke 1:31 God sent Gabriel to Mary to tell her she would conceive. You will conceive...
Luke 1:38 And Mary said, "Behold, I am the handmaid of the Lord; let it be to me according to your word." And the angel departed from her.
"I am the handmaid of the Lord....."
A handmaid is a servant. She had no choice since she was chosen by God. This is her honor. This is the sign of her blessedness. But, her permission was not required, it was preordained.
Certainly Mary declared herself a handmaid. She accepted. Gabriel did not label her as such. She self-described. A handmaid is a servant, unquestionably. Not a slave, and not a robot slave. She did, of her own volition, with the Holy Spirit already in her.
Preordained? Quite possibly. But the fact is that she, of her own free will accepted.