At the outset, I must note that your decision not to clerk for any firm or legal-related organization was not necessarily the most wise one. While several attorneys go to law school each year with the intention of not practicing law, your question indicates that at some point you likely may not have had a strong interest in the practice of law. For purposes of this question, we are going to assume you want to get a position in the best law firm possible. We will not be considering the road to government, public interest, corporate (i.e., in-house) employment since most new graduates such as yourself are interested in law firm positions.
As you are no doubt aware, it is quite common for students coming from top law schools like UCLA to work in some sort of legal capacity during their summers in law school. This is especially so during a law student's second summer. Legal hiring organizations hire summer associates because they want to get a sense of your work ethic, how you are likely to get along with other attorneys and whether they believe you are likely to make an overall valuable addition. There is also a great deal of competition for these summer positions-not unlike getting into law school. The type of summer position an attorney gets is often more important than their grades to their ultimate career direction.
In the absence of having held a summer position, many legal hiring organizations are likely to conclude that (i) you might not have been able to get a summer position, or (ii) did not have an interest in one. These are the most significant obstacles you will be overcoming in your job search. Due to the fact that you are coming from a top law school, these questions may very well be even more pronounced because it is far more common for law students from top law schools to work as summer associates than not. These issues, as well as your best strategy for getting a job, will be addressed in Sections A through C below.