Certainly. Nitrite is easily made, turning it into nitrate is the hard step. Your filter is, however, dead, and needs to be cleaned.
If possible, try to get an accilmatized filter, if not, change water daily. 50 % a day, for at least 3 weeks. After this three weeks you should be able to see the nitraite is getting less.
A tank normally requires only 2 weeks for cycling, but changing 50 % of the water daily reduces this. However, if you do not this weater change (you might even need more) the fish will not survive, nitrite is very toxic
For now - the most important thing will be the same water change - twice
I'm certain I would forget to turn the filtration back on myself, thus I keep it running while feeding. I have adapted the way I feed my fishes, and what I feed them