Yes, recently I applied for Software Developer fresh graduate position at Google from it's carerrs website and I got a direct interview call without any referral. So definitely you can apply from careers site. Just make sure that your resume is ATS compatible (yes mine was ATS enabled resume) and try to use maximum keywords which are mentioned in the job description.
I'd recommend you to first look for referrals on LinkedIn because it increases the chances of you getting shortlisted. If you don't get any referral then apply directly. Also, once you've applied through the careers site then you can't be referred for the same position again. So better you lookout for referrals before applying at their careers site.