How can I adopt my girlfriends 6yr old daughter when the father is around but doesn't acknowledge the child is his and has never had contact with the child?

1. Get married
2. Get a lawyer
3. Establish paternity.
4. Either get him to agree to relinquish rights or PROVE that he is an unfit parent. As an aside, going after him for child support is a good way to get him to relinquish his rights.
5. Start adoption proceedings.

In most areas, you have to be married to adopt as the other parent. The legal/bio father has to agree to the adoption or it be proven to a court that his rights should be terminated.

So your first step is to find a lawyer to handle this who can tell you the requirements.

I agree, first the child has a father, he may not be active in child's life, and he may not be listed on the birth certificate ( you did not tell us)

But there is a father, the issue is your local (state) laws if in the US. In general most will require you to be married, the bio father will need to be contacted and get him to sign his rights to allow adoption