Writing contests may or may not shorten your path to publication. If you win a legitimate one, it can add sparkle to your resume. Unfortunately, too many are just ways to raise money for the clubs that sponsor them.
Google the contest name and “scam” before you submit.
The link at the top of this post leads to an article that lists a few good contests. At least one has a deadline coming up soon.
Check the websites for submission details and follow all rules to the letter. Judges may (or may not) look for any excuse to toss out entries. It cuts down their reading time. To be fair, in their place, you probably would too.