First, I noticed "inerrant" doesn't seem to be much of a constraint when you are free to substitute different words and meanings as needed to arrive at whatever conclusion you wish to arrive at.
However, if God really said "make man in our image", and since man has three spatial dimensions and also a time dimension -- it implies God too had those characteristics, and therefore space and time DID pre-exist.
Of course, as I say, if you can redefine "image" to mean whatever you want it to mean, then the claim of "inerrancy" is a pretty cheap coin.
"Image" means shape, as in a mold was prepared within which to shape man, "Likeness" denotes understanding and intellect (Rashi). The two together mean that man possesses reason, free-will, and morality (Rambam).
Ari