People fall in love. That’s the best possible beginning anyone can think of. But then, sometimes they get married and that’s not a good ending 
. On a serious note, we have seen many times how two people in love manage to ruin their marriage afterwards. On the other hand, considering the other extreme, my parents did not even see each other till the time they were actually getting married. Certainly not a great beginning if we, in our times put ourselves in that situation. For me just thinking that is scary. But, that has worked out awesomely well for everyone involved. So what I am hinting at, is, that in my view this is a debatable statement. Moreover, it is very subjective to each person and the scope he is viewing it in.
For me, if I am making coffee I would surely like to begin well so that coffee turns out good because if something goes wrong in the beginning that cannot be fixed. In my view, as we broaden the scope to bigger areas such as life itself the statement cannot be taken as any mantra or rule.
The other point in contention is how you define the beginning and the end. What is the start? Is it the big bang days, the birth of a new life or the start of a day? In each of the cases that I can think of, the larger the time frame between the start and end time that we decide on, the more wrong the statement turns out to be. Big bang resulted in formation of earth but everyone now is ruining it. Birth of a new life always results in death years later. The point I am trying to make is that the wider the spread the larger the fallacy of the proverb.
Even in my professional life, I have seen projects start off magnificently and ending in disaster and on the flip side, projects stared with a bumpy ride and ended fantastically.
I thus believe that “Well begun is half done” is a more apt statement to make. Starting well puts you on the right track but that is only half the job done. There needs to be focus, discipline, passion and dedication to complete the endeavor on a high. That is the second half which more often than not people manage to screw up even after a good beginning.
For a personal anecdote, I did my engineering not from an institute which is the so called brand names, but have done decently well to be here at this point of my life.
Sachin and Kambli both had awesome beginnings to their career, but only one scaled the heights to reach the acme of achievements which just asserts my point that the proverb, at best, is very subjective with a lot of scope for variance depending on the person and context.
The counterpart of the statement would be better suited, which is, all is well that ends well. The focus of making a good beginning should be more importantly with a focus to end things well.
Beginning well sure is important, for it takes a lot of pressure of ending well away. If not for a good beginning, achieving a good ending becomes lot tougher. But as long as we manage to end things well, it should be good in most cases than not.
Everyone is entitled to have an opinion as the topic itself is very subjective in my view but I would like to end by saying that I do not know how I started on this topic and how I am ending this, but I have a feeling that, even that is not in sync with the topic . Rest is for you to decide.