If you log into your Adobe Stock, can you see the image listed in your 'License History'?
You should get instant access unless possibly a credit card issue or perhaps geographical location.
I logged into Adobe Stock, cleared by browser cache, tried 2 other browsers, restarted my system and logged back into Adobe Stock to still find the order 'processing'. I contacted my credit card company and they showed the transaction as authorized and approved. I was able to download the image four hours (4) after purchase. I certainly home that isn't the standard turn around time for a service that is supposed to be interactive, immediate and encourage collaboration. I'm working with a remote freelancer and the clock was ticking, as I was incurring expenses having to pay him while he waits on an image I needed to download. All the other stock photo sites allow instantaneous download access. I'll give Adobe Stock one more shot next time I need an image but I have to say this was not the best first-time experience from an Adobe product and I've been using Adobe products since 1992.
I am thinking that was just a one off occurrence or at least a rare occurrence as in 15+ images so far I have always had instant access. However, I am curious as to where you see 'Processing' in the Stock admin?