Success!
I have gone through character creation and played through the introductory part of Baldur's Gate 3. The load screen after the first portion of gameplay took a while - be patient. I bet there are others like it. I have no complaints aside from load times - performance is great, and there have been no crashes so far. Here is my system information. If your system is significantly different, you may have different results.
Ubuntu 18.04, Intel Core i7-2600K 3.4GHz, 16GB RAM, NVidia GeForce GTX 1660Ti, 1920x1080
Not an extremely high-end system, but a decent one. With the size of monitor that I like to use, there is no need to go to higher resolution.
Please note that people with AMD graphics cards have reported some issues. See Protondb for more information. It looks like using Glorious Eggroll's Proton fork, specifically, Proton 5.9-GE-7-ST might be a solution, but I obviously can't test this.
Here is what I did.
I installed it manually in its own Wine prefix, and I didn't load any libraries or do anything else unusual. It's big, so it takes forever to install. After installation, I added it to Lutris. I used Windows 7 mode, but Windows 10 mode probably also works. Normal Wine didn't work - it crashed when attempting to start character creation. The current release of Proton 5.0 on Steam worked perfectly. If you have installed Proton through Steam, Lutris will find it and you can use it for non-Steam games. Larian's launcher does not work - run the executable bin/bg3.exe directly instead. This is the Vulkan version. The DirectX version crashed after character generation and the following cut scene. I turned off DXVK in Lutris because it shouldn't be needed for the Vulkan version.
The launcher supposedly requires .NET 4.8. For some reason, .NET installation is broken in Winetricks on my system right now, and I haven't wanted to bother to install it manually yet. I might try it one day, but the launcher doesn't seem necessary. It wasn't necessary for Divinity: Original Sin 2 either.
I have not tested multiplayer, and I have no plans to do so, as the multiplayer option is of no interest to me. If others test it, I'm sure people here will appreciate reading about it.
I should have more time to play it this weekend, and I am looking forward to it. The introductory part of the game is quite dark, even for fantasy role playing games, and it is quite compelling. I expect to find bugs, as Windows users have reported plenty. If bugs rear their ugly heads, it might not necessarily be a Wine problem. At least it is working flawlessly so far, so I am optimistic.
Good luck to others who give it a try at this early stage. Again, results may vary depending on the system, so my good results don't necessarily guarantee success for everyone, and owners of AMD graphics cards might be in for a hassle. If anyone manages to get it to work with normal Wine, I'm sure instructions will be appreciated, as some people might not want to deal with Steam and Proton. For me, it isn't a problem - if Proton does the job, I won't argue with it, and I'm grateful to Valve for the contribution they have made to Linux gaming.