Most job postings stay active for 30 days, however, the time a job posting stays active depends on the company, the industry, the industry's employment rate and the position. It's best to apply for a job within a week or two of the job being posted to increase your chances of getting the job. The quicker you apply, the easier it is for the hiring manager to see your application and get in contact with you if they're interested. Though this is the best time to apply, you can also apply for jobs later than this date, but be aware that after two weeks the chances of getting the job typically decrease.
For your privacy and protection, when applying to a job online, never give your social security number to a prospective employer, provide credit card or bank account information, or perform any sort of monetary transaction.