In the English Grammar Profile, B1 point 5 in the category of discourse markers:
in writing, ORGANISING, MARKING NEW KNOWLEDGE, INFORMAL ‘you see’, ‘the thing is’
A search in the TLC shows that at B1 ‘the thing is’ is used, but ‘the thing is that’ starts at B2:
*We also believe conjunctions should be accepted ‘as you see’
PELIC STUDENT EXAMPLE:
Thai, Female, Level 3, Writing Class.