According to the Jewish Encyclopedia a free will offering does not involve any kind of compulsion whatsoever:
A term applied to gifts presented out of the benevolence or religious impulse of heart of the giver, and not in fulfilment of any obligation, promise, or vow. It is used as the term for the contributions of Israel to the construction and furnishings of the Tabernacle in the wilderness (Ex. xxxv. 29, xxxvi. 3); for the materials presented for the building of the First Temple (I Chron. xxix. 5b-9, 14); for the gifts for the support of the Temple service under King Hezekiah (II Chron. xxxi. 14); for the contributions toward the building of the Second Temple in Jerusalem, mentioned in the decree of Cyrus (Ezra i. 4); for the gifts of Israel in its own land toward religious services (Ezra iii. 5); and for the material wealth carried back by Ezra (viii. 28)...
Paul said that God delights in gifts that are given out of generosity rather than duress or ambition:
[2Co 9:7 ASV] (7) Let each man do according as he hath purposed in his heart: not grudgingly, or of necessity: for God loveth a cheerful giver.
However, genuine unselfish giving is not something that can be produced from an unregenerate heart:
[Jas 1:17-18 NET] (17) All generous giving and every perfect gift is from above, coming down from the Father of lights, with whom there is no variation or the slightest hint of change. (18) By his sovereign plan he gave us birth through the message of truth, that we would be a kind of firstfruits of all he created.