Could an elephant have the same momentum as a golf ball

No.

To understand the problem, we first have to analyze how momentum can be affected. Basically, momentum depends on how much stuff is moving and how fast that stuff is moving, as well. Considering the first factor, we can clearly see that an elephant's mass is significantly larger than the mass of a golf ball, despite the fact that they can possibly be moving in the same speed. Suppose that their momentums are somehow equal, this also means that the goft ball must be moving in an incredibly fast speed since p = m * v (which is nearly impossible).

Since momentum equals mass times velocity, a very slow-moving elephant could have the same momentum as a very fast-moving golf ball ... m/s because momentum is conserved.