How can I grow a beard fast? Vitamins, food, hormones?

Beard growth is not related to what you eat.  Beard growth is genetic and some men can't grow a beard. Your girlfriend probably likes the photo because it is of Ben Affleck, not his beard.  

Beard hair is a secondary sexual characteristic that many young boys and men wish to rush into. The notion is that a fuller beard makes a more 'macho' man, which is invariably a wrong one.
When does the beard grow?
Though the development of facial hair begins at puberty during adolescence, it is not until mid twenties to early thirties where a man reaches his peak in facial hair growth.
Can anyone have a naturally full beard?
The type of beard a man will have largely depends on his/their genetics. By having a look around the men in the family, the client should get an idea of what they should realistically expect in terms of fullness, pattern, thickness and texture.
Can a treatment help grow a beard faster?
If a patient's beard is sparse despite having good genetics, then there may be an underlying condition that can cause interference with the growth in facial hair. This could be hormonal, nutritional or an idiopathic (unknown) source like alopecia.
Depending on the condition, the patient may be prescribed with hormone treatment, nutritional supplement or other treatments like low level laser therapy, platelet rich plasma therapy etcetera.
However, if the patient has no co-morbidities then none of these can fasten beard growth.
Can anyone have get full beard?
Like the displayed photograph of an actor, there are patients who wish to look like them and increase their fullness. This is definitely possible using a beard transplant. It is a simple procedure that grafts the hair from your scalp to your beard.

Beard hair growth is influenced mainly by androgens (male type hormones such as testosterone, etc). There are no vitamins, foods, therapy that has been documented to improve beard hair growth - except androgens.Testosterone supplementation, whether by gel, injection, pill can certainly improve beard growth but has many, many "potential" side effects and is not recommended for most individuals.The best treatment for improving beard density is hair transplantation.You'd want to speak to an experience hair loss physician about all the options.Reference for InterestSaeedi M et al. A randomized double blind controlled trial of testosterone gel treatment vs vehicle control on the facial hair of young men with beta-thalassemia major. J Dermatolog Treat 2007; 18(5): 271-4

You will want to wait for age to help with your beard growth. Many men will only achieve a full beard in their 30's if they will get a beard. Look at your dad and uncles on both sides of the family for your expected beard growth.

Many young men want to accelerate their beard growth and ask
about it. It takes age (genetic triggers which occur in family lines) so
if you want to find out when your beard will grow out, you need to find out
when your father or grandfather started to grow theirbeard. Hormones should have kicked in
nicely by the time a man reaches 18 but he must wait out his genetics
as hormone alone are not responsible for the onset of beard grown. Beard
transplants can be done when the young man is a bit older (over 25) if the
beard has not grown in yet

There ie no medication that will help grow hair I the facial area. However you can try minoxidil and see if it helps.