Among the given options, the earliest event that occurred was Dinabandhu Mitra writing Neeldarpan.

Neeldarpan is a Bengali play that was written by Dinabandhu Mitra in 1858. The play depicts the exploitation and oppression of indigo farmers by British colonial planters in Bengal. This event is considered to be a significant milestone in the history of the Indian freedom struggle as it highlighted the atrocities committed by the British on the Indian people.

The other options in the question are:

1. Swami Dayanand established Arya Samaj: Swami Dayanand established Arya Samaj in 1875, which was a Hindu reform movement aimed at reviving the Vedic principles. This event occurred almost two decades after the writing of Neeldarpan.

2. Bankim Chandra Chattopadhyay wrote Anandmath: Bankim Chandra Chattopadhyay wrote Anandmath in 1882, which is a novel that depicts the Sanyasi Rebellion against the British. This event occurred almost a quarter-century after the writing of Neeldarpan.

3. Satyendranath Tagore became the first Indian to succeed in the Indian Civil Services Examination: Satyendranath Tagore became the first Indian to succeed in the Indian Civil Services Examination in 1863, which was after the writing of Neeldarpan.

Therefore, based on the above reasoning, it is evident that Dinabandhu Mitra writing Neeldarpan happened the earliest among the given options.