Is there possibilities that I could get hold of HR to discuss about my job application status? I tried contacting Walmart store as well as HR to get hold of them, they hang up on me. I am not happy of such unprofessional behavior.

I'll be honest, if you're not happy this early in the process, it's probably not going to get better for you. That's just my experience with a variety of employers. It's also a possibility the hiring manager (not always HR) wasn't at the store at the time you tried to contact them, and the customer service person answering the phone was indeed unprofessional. Perhaps try email and wait for a response. If you need a job immediately, lots of places are hiring, and have open interviews through the week.

It seems that Walmart hiring practice is all AI driven. Perhaps write(USPS) mail. Sounds old fashion but I get replies when pushing the issue

I remember when I applied to Walmart 12 years ago. I applied online but I went in person and ask to speak to a Manager or a Supervisor. It worked for me. I hope it will work for you too.

Amazon has been doing alot of hiring everywhere! Super easy to apply and they send you for drug test and such where is convenient for you and if all goes smooth, you will know your schedule and start date the day you apply. As long as the background and drug test are good...bam! You're in.