Trying to get into a company with great environment - any way to find unadvertised vacancies?

I have been trying to get into a mid-sized company (1000-5000 employees). They have a great environment and promote career growth. I have been contacting HR for a very long time and they are saying they don't have any fresher vacancy at the moment. Is there any way that I could get an opportunity at that company?

Hi

Why not you can gain some experience (in some small companies)related to that company and then apply for job with some experience?

If you have any known contacts in that company then appy through them as employee referral will be given some importance?