With the amount of content on the Internet growing exponentially every day, it can be difficult to determine which website should be ranked higher than another for a specific search term. The research-intensive answer is to find out when your website has the most traffic, and then submit your site to search engines when your traffic is at its peak.
The best time to submit to search engines is on the first and second days of every week. During this time, the number of people searching for your website increases, but the number of search results is still low. If you wait until the third or fourth days of the week to submit your website to search engines, the number of search results will be higher, but there will be a lot of competition for that traffic.
If you are worried about someone else submitting your site to search engines, the best solution is to get your domain registrar to do it for you.