Advice on Job Offer + Future Career Path (EE)

So, I am a new grad in Electrical Engineering and currently have an interest in software development. I am currently facing a dilemma and anyone who has been in a similar situation can maybe give me a hand:

I got an offer from a company that is mainly Mechanical/Mathemathics, however, the position is a Software Developer. The position is exactly what I want (software), however, the company isn't ideal for an EE grad. They have 0 EE working there, where most of their engineering team is comprised of Mechanical/Math PhD's. So looking at my future, I am kind of in a dilemma:

Pros:
-Software position
-Economy isn't great right now, so receiving an offer is a plus

Cons:
-Pay is much lower than my asking (20% lower)
-mech/math company


So clearly, there are 2 big cons, but on the other hand, I will gain software experience (although it will be mainly with programming for a CAD software). I do eventually want to work for a larger EE/Software company (IE. Amazon, Qualcomm, etc.) so I am wondering if this experience will help or hurt me.

Does anyone have any advice? I have only a couple days to decide.

Thanks!