I think, given what we know at the moment, there's really only one timeline placement that seems to fit right now. Let's go through all the possibilities:
SSTMCFSOoT/MMTPFSA
|ALttP/OoS/OoA/LAALBW/TFHTLoZ/TAoL
First, let's consider pre-OoT. This can easily be ruled out because Ganon didn't exist prior to OoT, and the Temple of Time was fully intact.
SSTMCFSOoT/MMTPFSA
|ALttP/OoS/OoA/LAALBW/TFHTLoZ/TAoL
Next, the Adult Timeline. Post-TWW is pretty much out of the question due to the Great Sea and all. The Hyrule we see in BotW is clearly Old Hyrule, so it can't be New Hyrule from ST, and I highly doubt this is a return to Old Hyrule post-ST with the Great Sea having been dried up. As for pre-TWW, well, the backstory doesn't give much room for BotW.
SSTMCFSOoT/MMTPFSA
|ALttP/OoS/OoA/LAALBW/TFHTLoZ/TAoL
Now to the Child Timeline. Ganondorf is sealed in the Twilight Realm for the entirety of time leading up to TP, so Calamity Ganon's presence in BotW would seem to conflict with a pre-TP placement. And in TP, the Temple of Time is more in ruins than it is in BotW, so it wouldn't make sense for BotW to take place after TP.
SSTMCFSOoT/MMTPFSA
|ALttP/OoS/OoA/LAALBW/TFHTLoZ/TAoL
And now we're at the time between OoT and ALttP on the Downfall Timeline, with Imprisoning War, Great Cataclysm, etc. ALttP's backstory does pose some issues, but it's also vague enough that BotW could very well work around it in some way. Plus, considering things like the state of the Master Sword, Temple of Time, Ganon, and races of Hyrule, this placement seems to fit best from what we know, and this is what I'm betting on.
SSTMCFSOoT/MMTPFSA
|ALttP/OoS/OoA/LAALBW/TFHTLoZ/TAoL
Finally, the end of time Downfall Timeline. There's not room between ALttP/OoS/OoA/LA and ALBW/TFH for another Link, so it would have to be either before or after TLoZ/TAoL if anywhere here. Given all the nods to TLoZ in BotW, a placement here does seem rather appealing, but there are some things that make it seem really out of place. Most notably, the appearance of various races in BotW like Sea Zoras, Gorons, Koroks, Gerudo, etc. These races are largely absent from ALttP on in Downfall Timeline, and it's somewhat hinted that these races may have either died out or become diluted into the Hylian race, with Rosso's Goron-like appearance in ALBW, for example. BotW's diverse Hyrulean population simply clashes too much for a placement this far down the timeline to make sense to me.
So yeah, post-OoT, pre-ALttP in the Downfall Timeline really looks like the most promising placement right now. Any other placement has too many other issues.