Many people get stuck in jobs they don’t like for long periods of time because it is difficult to find a new job when you work all business hours. You’re always working when it’s time you could be applying.
If it is at all possible for the industry and job position you’re looking for, use the internet. You can look for openings, research a company and position, and apply outside of business hours.
That takes care of the applying when businesses are closed part. What about your own mental and physical health? If you work full time, you don’t exactly want to overwork yourself while looking for your new job.
Set a reasonable goal, for you. It may be to apply to one job a month, or week. If you want to do more, then do more. Just make sure you have a goal and that it’s one that balances both your burning desire to leave and your healthy need for downtime.