I was hoping an expert on the subject would come in, but as none are forthcoming I would like to point out that this is actually a misconception, or more accurately, there is actually an exception to the unassuming historical maritime prowess of the kingdoms that used to exist in the Indian subcontinent. This exception is the naval invasions of South-East Asia by the Chola Empire.
The Cholas ruled over what is now South and South-East India. They were a supposedly ancient dynasty but there is little written evidence on the Cholas prior to the 7th century CE let alone their origins. However, we do have a number of sources on what is now called the "Medieval Cholas" or "Imperial Cholas". This began in c. 848 CE when Vijayalaya captured Thanjavur and later defeated the neighbouring Pandyas and Pallavas. The Cholas slowly grew their influence and power in the region but it was under Rajaraja I and his son Rajendra I that they became the dominant power in Southern India and projected their influence even across the Bay of Bengal.
Rajendra I or Rajendra Chola I became the ruler in 1014 CE. It can be said that his father, Rajaraja I, laid the foundations of a great maritime power by building a strong naval force and had captured the Maldives and the northern parts of Sri Lanka. This was made possible by commissioning various foreigners (prominently, the Arabs and Chinese) in the naval building program. These effort were continued and the benefits were reaped by his successor, Rajendra who continued his father's naval conquest of the whole of Sri Lanka in 1017. However, it was the conquest of Srivijaya - a kingdom in South-East Asia that would mark the greatest naval achievement of not only the Chola dynasty but all of the subcontinent.
Srivijaya was a thriving empire that controlled much of the Malay archipelago. They maintained a powerful navy which enabled them to control the region's maritime trade routes through the Straits of Malacca and that of Sunda. There are varying accounts of what caused Rajendra I to embark on his South-East Asian campaign but a plausible motivation is control of this lucrative trade route especially to China. The menace of piracy and the threat posed by it especially on the horse trade (on which the Chola Empire depended) was also another possible contributing factor. There are also those that suggest that the causes lie in the relationship between the Chola Empire and the Khmer Kingdom. The Khmer king Suryavarman I is said to have requested help from Rajendra I in his conflict with the Tambralinga Kingdom. This in return resulted in the Tambralingas approaching Srivijayan king Sangrama Vijayatungavarman for his support – triggering a conflict between the Cholas and Srivijaya.
Whatever the cause, in 1025 CE, the Chola navy embarked on their momentous naval campaign. Instead of entering the Strait of Malacca where Srivijayan naval forces were deployed, they sailed southwards along Sumatra’s west coast and entered through the Sunda Strait thus catching the Srivijayan forces completely by surprise. The Chola navy laid siege first on the capital city of Palembang, capturing it and plundering the Kadatuan royal palace. In the attack, Rajendra Chola is said to have captured and imprisoned King Sangrama Vijayatungavarman along with huge plunder. The Chola fleet then utilised the South-East Asian monsoon to their benefit – launching attacks on other Srivijayan ports, moving from one port to another swiftly thus, never really allowing the Srivijayan navy to launch an effective counter. By the end of the war, Rajendra had scored a decisive victory over Srivijaya and extended his supremacy over modern day Malaysia, the Andaman and Nicobar isles and southern Thailand. His dominance over the seas also allowed him to extract tributes from the rest of Siam and the Khmer kingdom. A second invasion was led by Virarajendra Chola, who conquered Kedah in the late 11th century.
The evolution of the Chola navy to become a true blue-water navy was a striking feature which was never matched again in the subcontinent's history. Though the invasions did not result in permanent occupation of the archipelago they did weaken the Srivijayan supremacy in the region and was one of the contributing factors to their eventual downfall.
An addition I would like to add (which is related to this question, especially if you are Indian and, thus, the reason for posting this very question) is there is a tendency in Indian media and to some extent in Indian school curriculum to portray India (and the kingdoms that used to make up the subcontinent) as having never invaded neighbouring kingdoms/countries in its entire history, which is not true. The naval expeditions of the Cholas is an instance proving this wrong. There are also the methods that independent India employed to incorporate many of the princely states after 1947 to name a few (albeit very few). Anyway, this is a different topic that merits a separate explanation but suffice to say nationalism and patriotism have been a major force in shaping this historical narrative.
Books:
In lieu of a more direct answer, I will show you to some previous answers that address Indian states with powerful navies and or sea-faring traditions.
This answer by u/LXT13OJ illuminates some of the history of the South Indian Chola Empire, probably one of India’s most famous naval powers.
Less related, but this answer by u/artfulorpheus touches upon the overseas population movements of people from what is now Bengal into Sri Lanka.