Does Flat Imply Finite?

There have been a couple of decent answers over the years but perhaps they could be expressed more briefly.

1. The existence of an initial singularity in a solution of General Relativity does not require that the early universe was infinitesimally small. It could indeed have infinite spatial extent at every time on every possible worldline (with “expansion” corresponding to reduction of density rather than increase of “size”).
2. Intrinsic flatness of space-time does not necessarily conflict with finiteness of space – related to the way a sheet of paper is intrinsically flat (in the sense of its own internal metric), even when rolled up into a cylindrical tube (which has finite “size” in the direction perpendicular to its axis).
3. Some claims of flatness for finite universes are only about the limiting behaviour for large time.

Source: (1001) Alan Cooper’s answer to I understand that the Big Bang was not an explosion which many people erroneously believe, but it was the start of space and time and our universe. However, if it started as infinitesimally small how can physicist say space may be infinitely flat? – Quora