I've got a copy of Jeremy Dupertuis Bangs' The Town Records of Sandwich during the time of Plymouth Colony, 1620-1692, (Leiden American Pilgrim Museum, 2014). Merry Christmas to me!! ;)
The first 3 birth records for Thomas Gibbs' sons are indeed not entered in the early pages of the town records, but inserted into the book among later entries in the 1650s. It isn't fair to say that they were entered later, as the birth entries are in a semi-alphabetical order that was akin to a dog's breakfast. The earliest clerk was apparently trying to organize births alphbetically by first name of the child, but later others entered names at random where there was space.
It's possible to say that Thomas Gibbs' children's births might have been entered at the time of their births, but there is no way to know due to the lack of any chronological order in this section of the records.
Also of note is that his name does not appear among the land grants that took place by 1641. He does appear in the "1643 list of names" (which appears to be those taking the oath of fidelity, but it is not spelled out).
So, although he did record his son's births in the town records as occurring in the 1630s, the first record that is dated clearly is in 1643 in the Plymouth Colony Records, Vol. 8:192.