First in Maharashtra

Kailash Temple, Ellora Caves

Government

First Royal Governor of Bombay State: Abraham Shipman (1662-64)
First Company Governor of Bombay State: George Oxenden (1668-69)
First Governor of Bombay State (Crown): Sir Bartle Frere (1862-67)
First Governor of Bombay State (Post India): Sir John Colville (1947-48)*
First Indian Governor of Bombay State: Raja Sir Maharaj Singh (1948-52)
First Governor of Maharashtra (After Bifurcation of Bombay State): Sri Prakasa (1956-62).
First Woman Governor of Maharashtra: Vijay Lakshmi Pandit (1962-64)
First Chief Minister of Bombay State (or Maharashtra): BG Kher (1947-52)
First Chief Minister of Maharashtra (After Bifurcation of Bombay State): Yashwantrao Chavan

Education

First University in Maharashtra: University of Mumbai (1857)
First Women Only University in Maharashtra: Shreemati Nathibai Damodar Thackersey Women's University (stard as a college in 1912, upgraded to university in 1951)
First Agriculture University in Maharashtra: Mahatma Phule Krishi Vidyapeeth (1968)
First Tech University in Maharashtra: Dr. Babasaheb Ambedkar Technological University (1989)
First Sanskrit University in Maharashtra: Kavikulguru Kalidas Sanskrit University (1997)
First College in Maharashtra: Poona Sanskrit College (1821; now known as Deccan College Post-Graduate and Research Institute)
First Engineering College in Maharashtra: College of Engineering, Pune (1854)
First Medical College in Maharashtra: Grant Government Medical College, Mumbai (1845)

People

Sports

First Individual Olympic Medalist from Maharashtra/India: Khashaba Dadasaheb Jadhav (1952 Helsinki Summer Olympics)

Awardees

First Bharat Ratna Award Winner from Maharashtra: Dr. Dhondo Keshav Karve (1958)
First Woman Bharat Ratna Award Winner from Maharashtra: Lata Mangeshkar (2001)
First Padma Vibhushan Award Winner from Maharashtra: Bal Gangadhar Tilak (1954)
First Woman Padma Vibhushan Award Winner from Maharashtra: Sumati Morarjee (1971)
First Padma Bhushan Award Winner from Maharashtra: Dr. Homi Jehangir Bhabha (1954)
First Woman Padma Bhushan Award Winner from Maharashtra: Pushpavati Mehta (1956)

Misc

First Session of Indian National Congress in Maharashtra/India: Bombay (1885)
First Passenger Train in Maharashtra/India: Mumbai to Thane (16 April 1853)
First UNESCO's World Heritage Sites in Maharashtra: Ajanta Caves and Ellora Caves (1983)
First Mega Foodpark in Maharashtra: Satara (2018)
First Cooperative Sugar Mill in Maharashtra/India/Asia: Pravara Sahakari Sakhar Karkhana Ltd
First Cotton Mill in Maharashtra: The Bombay Spinning Mill (1854)
First Nuclear Power Station in Maharashtra/India: arapur Atomic Power Station (Construction: 1961; Commission: 1969)
First Tourism District in Maharashtra: Sidhudurg District
First Metro in Maharashtra: Mumbai Metro

*Sir John Colville was the last British Governor of the Bombay State. His actual term started from 1943.