You could make instant coffee with regular coffee grounds but you need to use a filter to do so.
Put the coffee grounds into one cup and pour boiling water into the cup then stir it and let it steep for a few minutes then take a second cup and put a filter in the second cup and filter out the grounds by slowly pouring the coffee through the other filter into the cup.
It's not really instant coffee but it's bound to taste better and doesn't require a coffee maker to make.