Solomon was the youngest son of Bathsheba

People keep referring to Solomon as the oldest surviving son of Bathsheba, and Nathan as the second.

All three verses that list the sons of David and Bathsheba list Solomon as the last of the four and Nathan third.  2 Samuel 5:14, 1 Chronicles 3:5 and 1 Chronicles 14:4.

"And these were born unto him in Jerusalem; Shimea, and Shobab, and Nathan, and Solomon, four, of Bathshua the daughter of Ammiel:"

Also I personally don't believe the four listed here are only the "surviving" ones, I think even the one that died at birth was given a name, and that name was Shimea.

It is true that 2 Samuel 12:24 in context makes it seem like Solomon's conception happens right when they were done mourning the child that died, but these kinds of texts are not above skipping ahead, fast forwarding a bit.

Meanwhile verses that list children if anything are the opposite, they'd list them out of actual birth order only if it's to list the most important first, like Shem being listed first among Noah's sons in Genesis 5 when 10 confirms Japheth was first, or Abraham listed first among Terah's sons when there's reason to suspect he wasn't the first born either.

In 1 Chronicles 22:5 David emphasizes Solomon's Youth, the relevance to this dispute may be only a matter of a few years, but it could be Solomon as the absolute youngest of the options he was even considering was part of the point.

Among the things said by critics to attack the idea that Jesus had any claim to the Throne of David from Luke's genealogy is that the Throne could only be inherited through Solomon.  Solomon is relevant to II Samuel 7 because he is the near fulfillment, but nothing in Scripture says the Messiah must be descended from Solomon specifically, just David. On top of that go back to the account of the division of The Kingdom in I Kings 11.  It says Solomon's sons will never rule a united kingdom, only Judah.  The Messiah will rule all of Israel.  Meanwhile Zachariah 12:12 makes a reference to the House of Nathan that is interesting.  And 2 Kings 23:11 has a mysterious reference to a "Chamber of Nathan-Melech" Melech meaning King.