How does the 4th satellite in GPS know the time offset?
The satellite doesn't know your timing offset. GPS is a one-way street: the satellites basically only transmit their own time. Your receiver needs to do the rest, as the satellites can't know you even exist.
So, you really need to re-visit what you've learned about GPS so far!
Regarding the timing offset estimation: Don't consider the timing as a separate thing from the position. Instead, consider the 3 dimensions of your location and the time as one estimation problem with 4 unknowns.
All you get from your satellites is the time it was when they transmitted a signal. Your receiver hence only sees a time difference of arrival between these four. Only after solving the equations that gives all four unknowns by inserting all four time differences can you answer any of the questions of &quot;how far North am I? How far west am I? How high am I? What is the time?&quot;, and you can answer all of them. So, it's either &quot;all&quot; or &quot;none&quot;, not &quot;location separately from time&quot;.