You need to Extend the height and width of the added table in the layout view, it shows the records according to its size. If you want to adjust the size of the text in the added table in the layout view then go to Attribute table > Table options > Appearance, and modify the properties of the table, then add the table to your layout again.
In addition, you can select all records, then copy selected records and paste it in MS Excel, then copy it from MS Excel and paste it in the layout view(it will be pasted as an image). Doing this you can adjust the size of the table in layout view.
Image below shows how to copy selected records: