India doesn't need to round the good hope since it's on the East side. India subcontinent has a rich history of African trade.

As far back as first century CE, Aksumite Empire of Africa had trade relations with the Indian subcontinent that only grew over time. The silk road also touched parts of Africa.

Records show Western and Southern kingdoms and ports of the Indian subcontinent trading extensively with Northern and Southern ends of Africa through sea-routes.

As for actual colonization, mainly the Western states of Gujarat and Mumbai engaged in establishing actual colonies around (or before) 15th century on the East end of Africa, mainly in Zanzibar, Dar- e- Salam, and parts of modern Kenya and Tanzania. They mainly engaged in spice trade, but sometimes dabbled in slave trade as well.

Written record of the ancient Indian maritime history isn't well-preserved, and even less is translated in English. Most of what I have said comes from my personal readings of the maritime-history of the sailor- merchants of Gujarat.