I would actually argue that the replacement options are a lot more open than most people seem to suspect. Remember, giving a relatively obscure McDowell such a high commission, let alone command of his ad hoc army, was already unexpected and created some controversy with Winfield Scott, who notwithstanding liked him, and Joseph Mansfield over seniority.
My understanding is that at the outbreak of the war, the rising stars in the army were guys like McClellan, FJ Porter, WB Franklin, and Halleck. McDowell leap frogged all of them, and even rather senior guys like Mansfield, Sumner, Heintzelman, CF Smith, and others to get his appointment.
McClellan both at the time and in retrospect is the obvious guy to replace McDowell — he and Beauregard at the outset in particular were THE guys people were chasing after given their promise & prewar reputation.
In terms of alternatives, I would consider the following to be interesting, but not exhaustive, options:
Fitz John Porter - he had exercised considerable influence already in the Union army, and had been a vital officer on Patterson's staff. McClellan was his close friend and had already singled him out as an officer he wanted either on his staff or in command several months prior, and certainly after McClellan came east. By all accounts he was was an exceptional officer who in real life played a major role in the organization and direct training of the Army of the Potomac under McClellan (along with guys like Buell and Casey).
Joseph Hooker - I'm not sure if he was close to Lincoln at this point, but he was connected enough to receive divisional command under McClellan very early despite his reputation and trepidations from many regular officers. He had considerable strengths, many of which would have contributed to organizing and inspiring the army in ways similar to McClellan; however in terms of army politics he was probably worse than McClellan was, at least within the officer corps, and especially in relation to many qualified and capable professional officers. McClellan by contrast could maintain at the very least working relationships, if not devotion, with many talented officers who would have long careers with the army. That being said, Hooker may have been more aggressive in moving the army against Johnston before the end of the year, though this is just speculation, barring any primary evidence from him to the contrary about his preferences at the time. He certainly had a better relationship with Lincoln than McClellan (ultimately) which would have set him up much better in 1861-2 with many key the political actors in Washington.
Joseph Mansfield - An obvious choice. He had been leapfrogged by McDowell to take field command for the Bull Run campaign. A long-tenured professional, instructor, and engineer with the army, he also led troops bravely, if briefly, at Antietam. I suspect he would have had the approval of Scott and other regulars given his prewar seniority and background, though I confess I don't know enough about him personally to speculate on his ability and political relationships.
Edwin Summer - If I recall correctly I believe he was still out west at the time, meaning his command transfer would take some time. That being said, like Mansfield he had prewar seniority and responsibilities that clearly exceeded those of McDowell. He was also a veteran of Winfield Scott's campaign in Mexico and had the kind of gritty but professional reputation that seems like it would lend itself well to getting on with Lincoln. That being said, his actual performance in the army is definitely mixed, though he certainly had moments (Seven Pines comes to mind) that demonstrated even at his age he still had a real fighting spirit. Just really unclear though whether he had enough to really excel in army command, especially on an organizational level. His time in corps command didn't distinguish him in this capacity to my knowledge.
Ethan Allen Hitchcock - Another long-tenured officer and celebrated veteran of Scott's campaign in Mexico. Had previously resigned from the army iirc and come back in an administrative capacity. I believe he was offered commands on several occasions, most notably to replace McClellan in 1862, though he seems to have been uninterested (I assume due to his age). Nonetheless had he been chosen right after Bull Run given the emergency context, it's possible he'd be more open. He certainly had the administrative bona fides to have at least some success in organizing either the army or the forces in the theatre more broadly. No clue though what his effective skillset in command was and whether he was capable of effective field command.
Bringing the