but it doesn't make sense to me for such an old nation to have never tried to expand its territories.

India was not politically united for most part of it's history. The different kingdoms which existed mostly expanded at the expense of each other within India. It has formidable natural barriers on all sides.

In the Indian subcontinent lie some of the world's most fertile regions. In addition, due to the high population and periods of relative stability,trade and commerce within the subcontinent was flourishing.

When you compare that with the areas immediately surrounding India,

• Tibet - High altitude desert/ arid plateau
• Afghanistan- mountains and deserts
• Baluchistan- desert
• Myanmar- dense forests

Expansion was not very attractive in itself. There is a case for creating buffer regions(like Tang Dynasty did), but no empire was influential enough to conquer and fortify and hold the lands as buffer regions.

• In 305 B.C. the Mauryan Empire under Chandragupta went to war with Seleucus, one of the Diadochi of Alexander the Great. The exact events of the war are unclear; but it ended in a treaty where Seleucus ceded parts of eastern Afghanistan and Baluchistan to Chandragupta, in exchange for 500 war elephants, and a marriage alliance.
• Around 30 C.E. The Yuezhi were united into the Kushana state in modern day Uzbekistan~Kirghistan. They moved into India and conquered the lands of the Indo-Scythians as far as Ayodhya. The Kushan Empire had significant cultural influence from India, though it was a multi-cultural state.
• Around 730 C.E. The Karkota Empire in Kashmir, led by Lalitaditya Muktapida expanded into Afghanistan and central Asia, over states which had earlier been tributaries to the Tang Dynasty.
• Around 1030 C.E. The Chola Empire in south India invaded the Srivijaya Empire in the Malay Archipelago, possibly due to trade disputes. They established outposts and tributary subjects in the region.
• The Mughal Empire was established by descendants of Timur, who came from Central Asia. While it gradually became indianised, and in turn left an impression on India, it still had presence in Afghanistan until the time of Shah Jahan. They clashed with the Safavid Empire over Kandhar through many generations.

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But outward expansion was the exception rather than the rule. It is analogous to why the Roman empire(whose population and size of economy was comparable to the Indian Subcontinent) did not expand beyond the Rhine and the Danube. There was nothing much worth conquering. On top of that India wasn't politically united for much of history, unlike Roma.

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The most vital form of Indian expansion has been cultural. The concept of Greater India.

Due to long periods of prosperity, the region developed a high level of refinement and sophistication. This cultural influence was projected, in the west in Tibet, Afghanistan and sometimes Central Asia, and in the east, in Indo-China, and the Malay Archipelago, (Myanmar, Thailand, Laos, Cambodia, Vietnam, Indonesia, and arguably, Philippines too).

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Among others, the volumes of Ancient Indian Colonies In The Far East by R.C. Majmudar expand on this subject.