I'm not sure this is a good idea. The whole point of reputation is to measure how much the community trusts a certain user. New users that haven't done anything yet aren't trusted because they haven't done anything to prove that they should be trusted.
If all new users get bonus reputation without proving that they should be trusted, this could lead to abuse. For example, if the bonus would be 15 reputation, that would let any new user bypass the new user restrictions, making these restrictions ineffective. For example, spammers and trolls would get this bonus reputation and be able to immediately post 10 spam links in the same post and inappropriate images such as ads or Hitler porn. Newly created sock puppets would immediately be able to upvote posts from their main account, making is easy to earn reputation that you don't deserve (just create a sock puppet and upvote one of your posts, and create a new sock puppet for each post you want to upvote in order to bypass the serial voting reversal script). Even new users that don't want to do anything wrong intentionally may misuse their reputation by accident, for example posting a "thanks" or "me too" answer to a protected question or flagging an acceptable post as spam or offensive just because they don't know yet what's acceptable and what's not (if 6 new users do this, it would lead to an acceptable post being deleted and the owner losing 100 reputation). These are just examples of how giving bonus reputation to new users would make new user restrictions ineffective, I'm sure there are other examples.
If a user wants to get reputation, they need to prove that they can be trusted by posting good questions or answers or even by suggesting good edits. Even the first upvote (or the first two upvotes on questions) will unlock the basic privileges. Besides, users that are already trusted on other sites already get the association bonus.
Besides, if the point of your suggestion would be to encourage new users, I don't think it would be very effective. I don't think that reputation would encourage anyone if it could be earned for free. The whole reason why reputation is encouraging is because you did something to earn it: posted a good question or answer or suggested a good edit. On the contrary, if a user gets bonus reputation and then posts a bad question or answer that gets heavily downvoted would be even more discouraging since they would lose their bonus. It's better just to leave things the way they are, and then new users won't lose any reputation from their first downvotes since reputation can't go below 1. Currently, the only thing that would discourage them is that they didn't manage to post something that others found useful. With your suggestion, they would lose their bonus, which they would probably find even more discouraging.