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.
Hebrewa 9:
[27] And just as it is appointed for men to die once, and after that comes judgment,
Will your exercise of "free will" change this?