Sony San Diego acknowledged the issue via Twitter, noting it is "aware that some users are unable to download the PS4 game from the PS Store. We're working with the PS Store team to resolve asap." This is the series' first crack at the next-gen console following MLB 14's launch on PS3 and Vita at the beginning of April. "Thanks for your patience, we won't rest until you guys are playing," the developer added in another tweet.
We've reached out to Sony for more information on the issue and a timetable for its resolution, and will update as we learn more.
[Thanks to everyone that sent this in!]
Update: Sony added a note to its launch announcement post on the PlayStation Blog, which reads: "Due to unforeseen technical issues, MLB 14 The Show for PS4 is not currently available for download via the PlayStation Store. All parties are working as quickly as possible to remedy the issue. We'll update this post as soon as a resolution is reached. Thank you for your continued patience."
Update #2: In another update, Sony says the "PlayStation Store download issue regarding MLB 14 The Show on PS4 has been resolved. We apologize for any frustration this caused, and thank the community for its patience and understanding."