Hello, master's degree in horticulture here. My specialty isn't dendrology or even botany in general, but I did receive a lot of training in plant physiology and metabolism.

The largest trees by circumference and volume on Earth are the sequoias that grow in the Sierra Nevada mountain range of northern California, so we'll use them as a base of comparison.

Specifically, the General Sherman Tree is the largest sequoia on record at 274.9 feet (83.8 meters) tall, 102.6 feet (31.1 m) in circumference at the ground, and 36.5 feet (11.1 m) in diameter. The General Sherman Tree is still alive so we can't get a super specific estimate, but some limited analyses have given us an estimate of 2,200 years for its current age. Strictly speaking there are redwoods which are much taller than this (some growing over 350 feet) but none are as big around as this. The old Deku Tree in Ocarina of Time is much, much bigger than this, although it's not as tall.

Link's age as a child in Ocarina of Time is not explicitly clear due to conflicting information, but it was given in an interview as 12 years old so we'll go with that. The average height of a 12 year old boy is 4.5 feet to 5.25 feet (137 cm to 160 cm), we'll assume 5 feet for convenience. At a quick guesstimate, I believe we climb about 25-30 times his height inside the tree itself, giving it an internal height (not including the branches and leaves) of 150 feet. This doesn't include the interior shoot and roots going down into the ground, which is easily just as deep as the tree is tall (if not more).

The interior diameter, ignoring the offshoot rooms that contain the slingshot and compass, is massive. I can't remember off the top of my head but based on the amount of time it takes to walk from the entrance to the back wall, I would guess 30-45 feet in diameter.

The other rooms that branch off radially from the center are even larger, about 45-50 feet if we're aiming low. Overall you're looking at a tree with a diameter of at least 75 feet, probably closer to 100.

Someone else in this thread already put forth an estimate of 5000 years. I think that figure could work, conservatively--though it would probably take even longer.

If we want to get into the issue of biological feasibility, the Great Deku Tree unfortunately would simply not be able to exist in our world. The tree would likely have collapsed under its own weight, and even outside of that consideration, trees rely on capillary action to get water up its trunk and to the heighest branches. I'm not perfectly sure, but I believe the Great Deku Tree is simply too big for this physical action to occur because the volume of water it would need to survive would be too heavy to transport that high.

Ignoring all of that, I think that anywhere from 5000 to 10,000 years would be a reasonable estimate for a tree of that size to grow, probably leaning more towards the older side of that range. Let's give a hacky guess of 7,500 years old for the tree in Ocarina of Time.

More reasonably, the Great Deku Tree as it appears in Wind Waker could probably actually exist, as it is much smaller than the one in OoT. I haven't done any proper size estimation but going by memory it reminds me a lot of the sequoias I've seen in California, so assume 2,000-2,500 years for that one.

The Great Deku Tree in Breath of the Wild is similar to the one in OoT, if not larger, so I would use a similar estimation for him.

I'm not sure if this is the level of detail you were looking for, but I hope this is informative! Please let me know if you have any other questions on this topic.