Could someone point out the URL for downloading the ACS either single year or 5-year average data at the zip code level? There are about 45000 zip codes in the US so I expect to see the data file with about 45000 rows.
I've found that if you have the wrong set of filters on data.census.gov, it can prevent you from adding ZCTAs. This always seems to happen to me if I choose a table suggestion directly from the search box at data.census.gov/cedsci
What has worked for me is to go to the "tables" page (you may get there if you click "search" or type return instead of accepting a suggestion). Then, on that page, you should see "filter" near the top of the sidebar on the left. Click on that, and navigate as in the screenshot:
If when you get to "Zip Code Tabulation Area (Five-Digit)" you don't see options as in the screenshot, check "selected filters" below. Remove any that you don't actually need, as they seem to sometimes prevent the option from appearing -- or remove them all so that you can choose "all ZCTAs in the United States" and then, after that, build up the rest of the filters you need.
Hope that helps!