VC Lab and Decile Partners strongly recommend the following:
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10% is the minimum first close target size for funds that are $10m or larger.
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20% is the minimum first close target size for funds under $10m.
The key is to get the fund operational and to be able to fund its warehoused deals. Sometimes a fund may have to do a smaller 1st close of just shy of 10% so that it can get operational. If the choice is between being operational and reaching the desired amount, being operational is by far the most important (if within striking distance).
Attempting to do a first close significantly under these targets (particularly for a fund under $10M), may leave a fund unable to pay organization expenses and/or fund warehoused deals (to say nothing of deploying capital or how LPs might view things).
TL:DR - don't do it.
