What is kimchi "brine"?
This is not simply about water or liquid covering the veg, but brine (salted liquid) covering the veg.  The brine is necessary for fermentation and safety. I would worry that your rinse and soak steps washed away too much salt. There is no way to know for sure from your description.  When I make kimchi, I salt the cabbage, and leave in a colander overnight for excess moisture to drain.  Then without rinsing, I proceed with the rest of the ingredients. I pack into a container.  There is typically enough brine to keep the ingredients in liquid for the fermentation to proceed safely.  If you have kept yours refrigerated, eat it. If it has been at room temp, with low to no salt, I would be concerned.