Is the table level at the point the object departs?
There's a period of time where the object could "roll" on the edge, and its vertical veloctiy would not be zero at the moment it loses contact with the table.
If you are asking because you have seen it in a homework question then yes, they probably do mean (or it's safe to assume) the initial vertical velocity is zero.
To be sure you would have to post the question in case there is more to it.
How about you explain what you think, and tell us the context of the question, before asking us to do your thinking for you? ;)
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