During the episode, no date was indicated.
When Mother tells Jacob to go gather firewood because a storm is coming, does anyone else think this is the storm that brings the Black Rock to the island? Just because we didn't see the temple or the statue, doesn't mean it wasn't built.
During the time flashes, they flashed to when the Orchid well did NOT exist, but the statue did. During Across the sea, we saw a well, whether it's the same well, who knows.
If my theory is correct and Mother was killed in 1867, here is something interesting:
Mother and MIB die in 1867. MIB says he has lived with the "other people" for 30yrs. That takes us back to 1837. Before joining the others, MIB is confronted by the ghost of his mom. She says he came to the island with those people, 13yrs ago.(1824)
Wikipedia lists events from 1824. One of the first events listed is: "After much controversy, Michael Faraday is finally elected as a member of the Royal Society with only one vote against him."
Michael Faraday FRS (22 September 1791 – 25 August 1867) was an English chemist and physicist (or natural philosopher, in the terminology of the time) who contributed to the fields of electromagnetism and electrochemistry.
Faraday studied the magnetic field around a conductor carrying a DC electric current, and established the basis for the electromagnetic field concept in physics. He discovered electromagnetic induction, diamagnetism, and laws of electrolysis. He established that magnetism could affect rays of light and that there was an underlying relationship between the two phenomena. His inventions of electromagnetic rotary devices formed the foundation of electric motor technology, and it was largely due to his efforts that electricity became viable for use in technology.
Also note the year Faraday died, 1867
Coincidence? Maybe. But that's a big 3. Faraday, Electromagnetism, 1867. Also, the mention of the storm, Jacob wearing the same clothes, the math based on what MIB and his birth mother said...
It's not hard to imagine that over the next day or so, Jacob began to explore the island, moved to the Statue, discoverd his brother was now a smoke monster intent on killing him etc.. I'm a believer.