You would first solve for the center of the wrist.
There are examples on this website and textbooks how to solve for the center of the wrist. The wrist 3d pose ignores the last joint value because you are traveling along the Z rotation axis of the EE.
You can then solve for the joint value of theta 1 since it points the arm to the wrist center. (you should be able to figure this out).
Then, once you have t1 and the wrist center, you run into an issue.
It should be observed that you have 3 joints all on the same plane. (2,3,4) This means that there is a kinematic redundancy in this robot arm. I suggest you create your own solver to handle the planar kinematic redundancy. (The stretching out of the wrist). There are many ways you can do this, so you will just have to experiment.
I suggest starting with the simplest design possible.
This solver would have to take into account the magnitude distance from the 3d location of the center of joint 2 all the way out to the 3d position of joint 5 (wrist center).
This will allow you to solve joints 2,3,4.
This can be done by assuming the last link points directly to the wrist center (from joint 2). You can then solve for the other 2 joints (both solutions) through the inverse of the cosine law.
Then, once you have the joints 1,2,3,4 solved, you need to solve for t5 and t6.
If you do the FK given t1-t4, you know the 3d position of joint 4. Since you know the 3d position of joint 4,5,6, you can then solve for t5 using the 3d triangle shape. (sss form) Then, once you have t1-5, you can solve for t6 by subbing "0" into t6 with t1-5 and then doing an atan2() call.
This may not make a lot of sense, but you will have to do some research anyways.