I don’t think LaForge would want to be first officer. He already had his chance to be a captain and he went back to his engineering room. I would imagine that there are tons of good commanders out there wanting the spot, so promoting someone else so far down the ladder doesn’t seem likely, nor does Crusher.
La Forge would be the likely choice. He's gotta move his career forward at some point. Most likely, new character or transfer from another ship. If I had a choice, I'd like to see Tuvok became XO somewhere. He was aboard the Enterprise-E in Elite Force II anyway. You could also stripmine the SCE cast. Either way, I'd like to see a familiar character rather than a fresh creation.
I voted "Transfer from another ship," and while I think Picard would probably prefer someone from his crew, Starfleet would probably prefer someone from outside Picard's "comfort zone" after all of the shenanigans of the previous few years. They could assign someone over Picard's objections, but I think they would be more likely to give him five or six candidates to choose from, officers he'd never served with before, but officers Starfleet saw as their "best and brightest" and would benefit from serving under Picard and with his crew.
Strictly speaking, probably find a new officer - I think everyone else is comfortably set in their positions on the Enterprise proper, and, given the difficulty he had in the immediate post-Nemesis restructuring, I think he learned well that he can't just recreate the magic of the original crew of the Enterprise under his command. If Picard needs a new first officer, while he might have faith in his crew, he'd also take into account if any of them want or are ready for the position - of the options, La Forge HAD the opportunity to become a first officer, offered to him by Riker first off when he accepted command of Titan, even WAS a captain for a brief period, and came to the conclusion that he preferred being Chief Engineer, that he did his best work there, and it's likely a similar scenario for Crusher (plus Starfleet Command would probably raise several eyebrows at the idea of Picard's first officer being his wife). So I think that immediately puts both of them out of the running. They have their positions that they love and don't need to move outside of those particular roles - they're where they do the most good and have the most fulfillment right now, why change for the sake of keeping matters of promotion "in-house"? So dropping down to Konya, Trys, or Elfiki... I think Konya would move into the Security Chief position that Smrhova has left sooner than first officer, given his position as a deputy security chief, and Trys is not ready for the position (though if you gave her another five to ten years and ask again, I'd probably be willing to change my mind). As for Elfiki... She's a "maybe" in my book, but I lean more towards her not wanting the position. Granted, there's not a lot of development for her, but she seems to be good as a science officer, and wouldn't necessarily seek out the transfer to command that would come with that particular promotion. So I think that Picard's search would come down to having to bring in someone new. And, honestly, I'm not all that on board with the concept of "cannibalizing" from other lines - it's a bit too "small universe" for me to just trade around the same core group of characters in an organization like Starfleet, which has hundreds (if not thousands) of starships and starbases across even just the Alpha Quadrant alone. Plus it offers the opportunity for new avenues of exploration, by potentially bringing in some undeveloped species or characterization that hasn't been covered in depth.
Hmm, is Martin Madden still available? (Picard has never really dropped any hints about who Picard's first officer was after Riker left, has it? I wonder if they would mine that deleted scene if they ever needed to establish such a thing?) This is probably what would happen in the Starfleet "reality". But I think it would be interesting story-wise if Dygan was given the position. Another option I would like would be Kadohata, if she were to decide to return to Starfleet. Neither of which really fit the poll options, sorry.
Ooh I like the idea Kadohata comes back. It's been 6 years since she took detached assignment to the displaced persons' agency, she did that to be closer to her kids but they might be old enough to be leaving the nest now and she might love the chance to be XO under Picard. He loves XOs that are brave enough to challenge his authority when they disagree with him strongly. She has that in spades.
Spoiler: Coda Book 3 No. To use Steven Moffat's overworn phrase, though, it's timey-wimey. The First Splinter has a future that extends beyond 2387 (The Good That Men Do, for instance), but it also ceases to be in 2387. I don't see those as incompatible. It exists. It doesn't exist. It never existed. Time is strange.
In fairness, one could interpret the ENT Relaunch novels, including the 25th Century segments of The Good That Men Do, as being from a different timeline than the First Splinter, as nothing explicitly establishes them as being the same timelines.
I do appreciate you spoiler-coding your initial response, but then your open paragraph directly mentioned the very event your initial response was referring to. Rather than try to piecemeal spoiler code bits of your paragraph, I just extended the spoiler tag to cover everything. We are still within six months of release of Coda Book 3, so the events of that novel are still under spoiler protection. @Sci , your post did not mention anything that happened in the novel, so your post was only edited to put the quoted text under spoiler code. Your text has not been altered.