This represents a misunderstanding of the text. Paul clearly states in v. 24 that this is allegorically speaking, that the women Hagar and Sarah represent the two covenants, the law, and Christ's new covenant.
You must be careful to apply the allegory to what Paul actually applies it to rather than using it as a broader brush to apply it to everything Paul is speaking about. I believe that is precisely where you interpretation fails for several reasons.
For example verses 22-23 MUST first be understood and accepted literally and historically not allegorically. The allegory is the application by Paul to these literal and historical events in verses 22-23 which in no way denies their actual literal and historical occurrence.
22 For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman.
23 But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise.
The Specific allegorical application is then stated in verses 24-26
24 Which things are an allegory: for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Agar.
25 For this Agar is mount Sinai in Arabia, and answereth to Jerusalem which now is, and is in bondage with her children.
26 But Jerusalem which is above is free, which is the mother of us all.
Also, please note that "sinai in Arabia" is placed in contrast to "Jerusalem which is above" rather than to "the cross" as your position supposes. Significantly, Sinai in Arabia and the new "Jerusalem which is above" were conexistent prior to the cross as well as now rather than one then and the other now as your interpretation demands. More importantly, Sinai as a covenant was not existent at the time of either Ishmael or Isaac as they lived 400 years prior to when that covenant was given.
However, the truth is that the essence of the Sinai covenant, just as the essence of the covenant of the New Jerusalem have always existed from the garden of Eden and have always been two fundemental ways (Mt. 7:13-14) called "works" and "grace" and even long before Isaac, Noah "found grace in
the eyes of the Lord" under the "everlasting covenant" or what is called now confirmed on earth by the blood of Christ as the "new" covenant, not because it presents a new way of salvation but because it was publicly ratified by blood AFTER the Mount Sinai covenant was ratified by blood. However, it is the "everlasting covenant" (Heb. 13:20) as the "new Jerusalem which is above" existed BEFORE the giving of the "old" covenant at Mount Sinai and remember it is described as "the blood of the everlasting covenant" which preceded the blood which established the Siniatic covenant.
However, your interpretation has even greater problems as it denies the possibility of new birth until after the cross, and most likely until Pentecost when Jesus BEFORE THE CROSS not only teaches it as a necessity for fallen man in John 3:3-6, providing only two possible alternatives "born of flesh" versus "born of Spirit" (Jn. 3:6), but rebukes Nicodemus for being a teacher of the Old Testament Scriptures and not understanding this very necessity (Jn. 3:9). Hence, the very same alternative births in Galatians 4:29 are confirmed BEFORE THE CROSS by Christ in John 3:6 as the only TWO POSSIBLE ALTERNATIVES, whereas your interpetation and position demand NO ALTERNATIVE to being born of the flesh prior to the cross.
Moreover, this is only the tip of the iceberg of the problems your position has, as your position demands that prior to the cross those "in the flesh" which is equal to be "born of the flesh" could please God and walk by faith (Rom. 8:8; Heb. 11:6) which is impossible.
Finally, Galatians 4:29 is not stated to be allegorical but is stated unequivocally to be understood and recognized as a contrasting condition of NATURES due to two different births both then and now, just as Jesus BEFORE THE CROSS confirmed two different births (Jn. 3:6) using the PRESENT TENSE not the future tense for either, as your interpretation would demand.