If there is a God, it is my philosophical belief that we cannot understand how he is timeless or eternal. And that is applied to everything that could be timeless or eternal (whatever that means), since our mind are limited and "programmed" (by intelligent design or evolution or even something else) to think is certain limits (in this case to think "within" spacetime).
Beeing myself a physics student, i have no idea what time is. And that is because within physical and mathematical definitions of time, there's still a lot of space for philosophical interpretations.
Mathematically (in which definitions are somewhat generalized to every possible logical situation) time can be considered eternal. You can say that time start in minus infinite and will stop in plus infinite. In that kind of thought, you can say that, even if there isn't motion in the universe, there is still time (or it would be if mathematicians could think without time xD joke). Physically, as far as i know, time is more "thing" to which you can compare motions. I'll try to be more clear (please excuse me, English is not my primary language). Time is "only" (i might be wrong here) useful to measure motion. We use it to know which things happen faster or slower. So, if we think a little, in a physical definition, if there is no motion, there is no time, if there is no time, nothing happens so on could say that everything that exists in that no time situation is eternal. So something timeless would be something eternal/never changing and eternity would be the lack of time (time wouldn't be within eternity, but rather they would be two (and i don't know it is correct to say this but) "different" yet related things).
Anyway, can God be timeless (whatever that means)?
Every argument that i thought until know doesn't answer successfully that question, probably because i cannot think outside the box that is spacetime. He might be, he might not be. He might be sometimes, He might be always, he might be never. We might never even know exactly what timeless is. Same way scientist say we probably never know what existed before the big bang, before time, same applies to God here. I can only conclude that if there is a God as described in the Bible, we cannot understand everything about him, and i also believe that we cannot understand this question about him in particular.
I might be wrong, and that's why i shared my knowledge here, so you might use it to correct me, or even correct my knowledge itself.