1.3s imo is a fine time frame to start actually speaking. Humans, well most of us anyway, don’t start speaking informative words right away. Instead we add in “umm”s, inhales, “mhm”s, “yeah…”s and so on.
I think your approach is a good one. I’m now wondering for these filler sounds, do you contextualize them somehow? That is make filler feel more natural.