So at this point, I'm sure a lot of people have already noticed that Titans have wings, and pretty big ones as that. Considering their size and presence, they were probably actually using said wings to fly. Which well, begs the question: How the hell would you even be able to get a living creature the size of an island into the air?
Short answer: Well you don't with actual physics. But this is a magical world so we can fudge the rules a little bit. But we can also do a little bit more informed speculation rather than just say "well it's magic" and leave it at that. And based off what we know, I do believe there are potentially two things that would have allowed such a giant creature to become airborne.
The first bit is that they might have employed the "quad launch catapult" seen in pterosaurs. Unlike birds, which launch off the ground with just their hind legs, pterosaurs launched off the ground with all four limbs. The bulk of the launching power coming from the forelimbs, which are the wings in this case. This is a much more efficient way to launch a large animal into the sky, since the muscles used for launching also happen to be the same muscles for flying. It's how the largest pterosaurs easily dwarf even the largest flying birds to have ever existed. While the large flying birds and even airplanes require a runaway to gain enough speed and lift in their wings to soar into the sky, a pterosaur the size of a giraffe can launch itself soaring straight into the sky from a standstill in a matter of seconds.
However, even with magical physics, a quad launch alone might not be enough to launch a fully grown Titan into the sky. This is where the other bit comes in: The fire glyph. We see Luz use the fire glyph as a means of propulsion, and a pretty good one at that, from just a piece of paper.
So imagine the power of a fire glyph from a fully grown Titan. At that point, you have a proper rocket.
So using those two bits of knowledge, we can potentially see how even a full grown Titan could launch itself into the sky. Employing a quad launch like a pterosaur, it pushes off the ground with its powerful wings in a sudden burst of energy, right before activating several fire glyphs (either around the trailing edge of its wings, or from its palms and feet, etc.) to further gain altitude into the sky. Once up there, its wings can catch enough air to let it soar across the sky with little effort. And should it begin to decline in altitude? Well large soaring animals tend to seek out thermals, currents of warm air rising from the ground, to push them back into the air.
A Titan however, might not need to seek out a thermal. It can just create its own thermal. All it needs to do is use those fire glyphs to heat up the air beneath its wings to keep itself in the air for as long as it wants.
So how would a Titan get itself into the air? Well we ultimately don't know and the canon explanation would probably just be "magic", but I like to think it's basically like a Rocket Powered Pterosaur Catapult.
