I have seen a few of these types of graphs from Jean Laherrere in his Lisbon talk and they all seem to spike at the beginning, whether they are for individual fields, US states, or even countries.  It is probably the nature of an oil field itself.  Initially the gushers at the beginning force high production with their high pressure, but then things settle down into a steady pumping 'rhythm'.

Remember, the graph is not a graph of time, and the 'early' values depend heavily on accumulated production, so small 'inaccuracies' at the beginning are heightened.

It is not unlike the 'estimated time left' calculation that is done when you download a file.  In the first few seconds the estimate can go all over the place, but then it settles down to a fairly steady rate.

Both the US and the world graphs don't settle down until cumulative production reaches about half way to peak annual production (at the upwards inflection point in an annual production versus time graph). Also, the early distortions are in both case systematically above the linear trend once it appears, not randomly above and below. So I think we need a more powerful explanation than you propose - it appears there might be some systematic correction to the model needed to explain the early years better.
I guess the question is, where did the EIA get this early data from?  Was there any financial benefit to US producers in the early days to over-estimate production and under-estimate cumulative production?  Perhaps there was a timeliness issue about the reporting of early cumulative production - i.e. they reported them later.

I would say that given the fact that a lot of that early data would have been in the first half of the 20th century, that it's reliability would be questionable, compared to the accuracy of data resulting from the second half.

Anyway, the more settled data later is just that, settled, so I would tend to believe that was more the 'norm'.