It doesn't necessarily place the games in one particular timeline. We see far too much to contradict one timeline placement. We are also told (in Creating a Champion, I think) that the current Great Deku Tree was conceived as a tree that grew near the Master Sword, and was changed by the Sword's power. We only see one noteworthy tree planted close to the Master Sword, it's seed looks an awful lot like a deku nut, and it's planted back in SS. Be it the Life Tree, or not, the conception leaves room for all time lines, due to the tree's creation being tied to the Master Sword, rather than being connected to a previous tree.
We also see large intelligent talking trees in the Oracle games, so having more than one is not an issue. And, neither is having them in timelines other than the adult.
Additionally, I have pointed out that the Ash Swamp (BotW/TotK) lines up with the Lost Woods (OoT). The name and the remains (particularly in BotW) suggest a large forest fire. The water fall at the Dueling Peaks Stable is bang on for the waterfall in the Kokiri Village. The well at the stable is the only one I could find that is made up of multiple chambers, leading down (much like the inside of the Deku Tree in OoT), and there are fairies at the bottom (which is also a bit unusual for wells). We have Koroks, not as a timeline cue, but because the home of the Kokiri is gone.
I think the one we met in OoT is gone, and the one we know now predates that one. It is even easily possible that the one we met in OoT was born from a seedling of the one in BotW/TotK.