After the 2020 election, there were a number of surveys that asked if you wanted Trump to run again in 2024. I compared the results for similar surveys about Gore running in 2004 and Kerry running in 2008.
The years in the x-axis are 1 for the first year after he lost, 2 for the second, etc. The y-axis is percent saying yes minus percent saying no. Trump is consistently below Gore, and about the same as Kerry. That is, he didn't have an especially large base of support among the voters.
These figures are based on the whole population, but some surveys limited the question to supporters of the candidate's party.*
Compared to Gore and Kerry, Trump looks stronger within his own party. But another losing Republican candidate, Romney, got about the same results as Trump, suggesting that maybe Republicans generally are more willing to consider second chances.** In any case, Trump's value of +30 means that about 35% of Republicans didn't want him to run again, and wanting someone to run again doesn't necessarily mean that you will support him. So there was definitely an opening for other candidates.
Turning from voters to elites, here are endorsements from Republican senators and governors (data from Ballotpedia).
Trump announced his candidacy after the 2022 elections, and within a few days picked up his first endorsement (from Tommy Tuberville). Then there was a cluster in early 2023, and some more in April. By April 17, he had 10. Then other candidates got some endorsements, and by June 21st the gap had narrowed: 10 for Trump, 6 for others. After that, Trump pulled ahead: 32 endorsed him before the Iowa caucuses, six more before the New Hampshire primaries, and another 10 before Nikki Haley dropped out. Out of a total of 76 governors and senators, 44 endorsed Trump and only 11 endorsed other candidates (four of those endorsed Trump after their first choice dropped out, so 48 endorsed Trump before the race was settled).
My overall conclusion is that "the base" didn't impose Trump on Republican elites; Republican elites asked for him. That leads back to my original point about Trump's poor record in general elections--why would professional politicians want a weak candidate at the top of the ticket? One possibility is that they thought his electoral record was actually a good one--I can imagine an argument along those lines. Another, and more disturbing, possibility is that they looked at the candidates and thought that Trump would be the best one to lead the country.
*Partisan breakdowns could be found or calculated for some of the surveys of the general public, but I'll leave that to someone who has a research assistant to do the work.
**This seems plausible to me--my impression is that when Democrats lose, they blame their candidates; when Republicans lose, they blame outside forces (especially the media).
[Data from the Roper Center for Public Opinion Research]