I really value this question and the answers. Fully appreciating the "who you know" variable in start-ups is so important.
The credibility of the team is an important part of the overall decision to invest. An an investor in the high-risk world of start-ups with such a high failure rate i want to mitigate my risk as much as possible.
Google was used as an example -- but even there the primary investor made brining in "adult supervision" as part of the contingency of their investment.
There are many ways to augment your team. These include building out a preliminary board of directors of experienced and connected individuals. Another is building an advisory board of people who lend their names and networks.
I think that building a network of supporters and stakeholders that carry credibility among your target (whether funder or customer) is an important part of building a successful company. Your ability to build that network will be understood as a reflection of one of your abilities to make your star-up successful.
I wish you the very best in building that network!