God the Father didn't become incarnated into a form of human being, but as you have rephrased, yes, it was His only begotten Son Jesus who was conceived by the Holy Spirit and born of the virgin Mary. The same God that said "Let there be light," also sent us His Son to save us from our sins.
I'd rather people rest on the Scriptures rather than my writings, so that the Word of God can find fertile ground in their hearts and produce faith for them to accept the truth of Christ's divinity and His humanity in the Godhead.
Col 2:8-9 Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ. (9) For in him dwells all the fulness of the Godhead bodily.
Mat 1:18-25 Now the birth of Jesus Christ was on this wise: When as his mother Mary was espoused to Joseph, before they came together, she was found with child of the Holy Ghost. (19) Then Joseph her husband, being a just man, and not willing to make her a public example, was minded to put her away privily. (20) But while he thought on these things, behold, the angel of the Lord appeared unto him in a dream, saying, Joseph, you son of David, fear not to take unto you Mary thy wife: for that which is conceived in her is of the Holy Ghost. (21) And she shall bring forth a son, and you shalt call his name JESUS: for he shall save his people from their sins. (22) Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying, (23) Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us. (24) Then Joseph being raised from sleep did as the angel of the Lord had bidden him, and took unto him his wife: (25) And knew her not till she had brought forth her firstborn son: and he called his name JESUS.
Rom 1:3-4 Concerning his Son Jesus Christ our Lord, which was made of the seed of David according to the flesh; (4) And declared to be the Son of God with power, according to the spirit of holiness, by the resurrection from the dead:
Enough for a sceptic to search their heart about . . .