Help a newbie! Needles too short?

Okay I’m a veeery beginner knitter. I’ve made some dish rags, sort of. Just squares, or you know, things resembling squares! :wink: Anyway, I’ve decided to venture into the world of baby blankets. I found this great, simple pattern that’s just in garter stitch. The problem is, it says to cast on 135 stitches on a size 13 needle, then switch to a size 3 every 7 rows, etc. What I don’t understand is my needles aren’t long enough to hold all the stitches? So what do I do? Any help would be appreciated.

You could use circular needles and just use them like straight ones. There are circulars that are a meter long and the stitches should fit on them.
I mostly knit with circulars even if the stitches would fit on my straights, cause the weight of the knitting is then in the middle.