Can I Escape Est Taiyar without portals?

I had the same problem, and luckily there is a way to get out, but it involves a lot of precise platforming.

You jump up small ledges and holds. It took me about an hour of pressing B, and making and reloading saves, and dying.

But there is a path to jump up and out.

You start with using Aard on some stalagmites, getting on top of the broken pieces, then jumping up to a cliff, across to another cliff, around a broken bridge, then up some rocks, out through a wall. Then you jump up, to drop in through the ceiling of the level you can walk out from.

According to this forum post this user is having the same issue you were. It looks like there may be destructible walls in the area you're in. Use your Witcher vison to find the cracked walls and then use your Aard magic to break through it. This should open up a passage to help you traverse the ruin.

If you still are stuck, and are playing on PC you can press either your ` (tilde key) or F2 to open the console commands menu. Enter a console command such as gotoNovigrad to be teleported away. Note that using console commands may invalidate Steam Achievements for this playthrough.