While more can be said, How old is Hinduism? written by u/wotan_weevil may be interest

To answer this questions we must first answer another. What is Hinduism? Now, there are many ways of approaching the topic since the diversity of thought in the Hindu tradition as well as scholarship on the matter, prevents us from arriving at any one singular, rigid definition to begin with. There are regional and philosophical variations in belief systems, rituals, socio-political and cultural implications etc. It might help us if we work our way backwards with our definition, first by understanding how or why the word "Hinduism" is used to describe what we understand to be Hinduism and then trying to date what we understand as Hinduism by looking at those commonalities which might connect regional variants to form an overarching whole.

So, first and foremost, the words "Hindu" and "Hinduism" must be placed in their historical context and their meanings and usage understood. We can first turn to Asko Parpola, The Roots of Hinduism : The Early Aryans and the Indus Civilization. We find that the origins of the term "Hindu" go back to early 6th century BCE, when the Persians conquered the Indus Valley. The Indus is known as Sindhu in Sanskrit. The Persians replaced the "s" for an "h" and therefore this newly acquired province became Sindhu. The Greeks pronounced this word as Indos and in Latin this becomes Indus, and the country surrounding the area became India. When the Mughals conquered Northern India in the 16th century CE, they called this country to the north of the Narmada, Hindustan and the people Hindu. This was the terminology that the British adopted, as Hindoo, when they came into contact with the Empire and learned of its people and culture. And in the 20th century, the word Hindu became a common label for all those Indians who weren't Muslims, Christians, Jews, Parsis, Jains or Buddhists. As early as the 18th century, we have an instances of merchants and evangelists that arrived to the shores of the Indian subcontinent along with the EEIC, such as Charles Grant, who used the term Hinduism for the older Hindoo religion or Hindoo creed. Similarly, Raja Ram Mohan Roy used this terminology in 1816-17 as well. In the 19th century, Hinduism came to be used as a general term for all those religions or religious practices that were native to the subcontinent with the exception of Sikhism, Jainism and Buddhism.

At this point we more or less have a working definition and timeline, as to when the words and phenomenon that we are concerned with, were used and what they implied. But now having established a timeline and definition, we find ourselves confronted with another question as to what constitues Hinduism? For if we can establish what these components that make up Hinduism are, we can trace their timeline, independent of the terminologies used to label them, to establish how old these components are, that we collectively refer to as Hinduism. Opinions are divergent as to what Hinduism is constituted of, and whether or not these components qualify collectively as a religion. Therefore, before we begin we can first state what doesn't constitute Hinduism. Hinduism has no founder, no fixed canon which succinctly embodies its major beliefs and practices, no organised priesthood as is understood in the context of other major world religions. As Upinder Singh states in A History of Ancient and Early Medieval India from the Stone Age to the 12th century, that given the diversity of beliefs, traditions, rituals and sects, Hinduism has often been referred to as a set of socio-cultural practices, rather than an actual religion, or as a phenomenon inextricably linked to the existence of caste, while there's also the idea that Hinduism shouldn't be seen as one singular religion but rather there should be talk of Hindu religions. To allow for the possibility of an answer to our question, we can follow the theme we have established earlier and trace our steps backwards, by first looking at the commonalities among the various forms and sects of Hinduism today and try to work our way back in time to trace when these commonalities emerged and try and establish a timeline. Keep in mind, there will be disagreements as to the basket of commonalities that ought to be picked for this exercise, in fact, there can also be disagreement as to whether this exercise is even the appropriate instrument to answer your question or not. Leaving room for critique and disagreement, let's move forward. If we observe Hinduism today there are certain elements that we find to be intrinsic, and largely prevalent throughout the length and breadth of India :

1. The idea of a personal God, once which provides an intimate connection to the divine and a personal salvation.

2. The importance of mandirs or temples and idols.

3. The scriptural recognition of the institution of jati as a concept

4. The important postion of ceremonies and rituals that form a central part of Hindu life and are considered necessary for the progress of one's life.

TEMPLES :

Temples have played an important role in forming social structures and in shaping economic, cultural and poltical phenomenon throughout Indian history. Temples were centres of social activity and occupied an important role in the political considerations of rulers. Temples allowed rulers to express their own beliefs or their populace, they allowed for people to acquaint themselves with one another, made for areas for the performance of important social ceremonies and rituals such as the "sacred thread ceremonies" and marriages. Temples also played a role in urbanisation, since with the creation of large temples and temples complexes rulers created the economic basis for town formation. Physical structures that would naturally be centric to societal concentration and the intial villages of labourers employed in the construction of these structures provided for economic stimulus to local markets, therefore boosting town formation and urbanisation throughout the first millennium CE. According to Upinder Singh in A History of Ancient and Early Medieval India from the Stone Age to the 12th century,

... Mention in the Baudhayana Grihyasutra (2.3.13) of the worship of deities in connection with the ceremony of the first outing of a newborn child from the house. The Gautama Dharmasutra (9.12-13,45) alludes to images of the gods in the context of rulers for a person who just entered the householder stage. Patanjali's Mahabhasya mentions images of the deities Shiva, Skanda and Vishakha. The Arthashastra (2.4 17, II.4.19) recommends that the temples dedicated to the guardian deity and the family deity of the king should be located in the centre of the city. It also advocates the building of temples dedicated to the deities of the four quarters at the four city gates. This text mentions shrines for the tutelary gods or various groups of people as well as in storehouses. There is also mention of temple property, including images, crops, cattles, slaves, fields, houses, money, gold and coins. The earliest inscriptional references to and archaeological remains of Hindu temples belong to c.200 BCE - 300 CE.

Therefore, we can date temples to as early as roughly 200 BCE. That's one component down.