Yesterday, I got an email from someone at a company that I applied to. Almost an hour after applying. They said they were interested in phone interviewing me "later this week." I responded to their email and sent over my availability. Come today I have not received a response which is peculiar to me. If they don't respond by tomorrow afternoon or Friday should I ping them or just forget about the opportunity?
Simply put, contact the company again.
Preparing for an interview takes time. It could be that the interviewer needs to free a time slot in what could be a very busy schedule. Or it could be that the interviewer is preparing a set of questions to ask you. Honestly, there could be thousands of reasons as to why the company hasn't responded to you yet, it's your job to find out, professionally, in a follow up email.
Something along the lines of:
I was contacted by X who was wanting a phone interview with me. We are still in the stages of scheduling the interview and was wanting to know if the decision on a time slot has been made?
My available times are listed below:
Make sure to include your availability again and make sure you are actually available on those days, otherwise you both could end up with some difficulties1.
They obviously think you're a good candidate, I mean, you were contacted a mere hour later after applying. To show them that you are an even better candidate, let them that know that you are definitely interested in the job with some follow up communication.
It's always best to ask questions and learn more than to stay in ignorance, even if the questions sound daft to you.