The Vedic Aryans themselves weren't a race. They were a group of Indo-European tribes, & those collective tribes originally constituted a race. By their description, they were fair skinned, good looking, tall, & well built people. There are multiple tribes mentioned in the Vedic scriptures, such as Ikshvaku, Ayu, & the Alina people, etc. The Indus Valley Civilization was already destroyed with its population being severely reduced by climatic conditions according to modern accounts. You seem to have a wrong idea of the term "Aryan Invasion". Aryan invasion does not mean that massive hordes just attacked out of nowhere & shook the whole Sub-Continent. It was most likely a minor invasion in the beginning as described in the Vedic scriptures themselves, & after that period the Indo-Aryan tribes migrated in groups towards the Indus. Based on my readings, it seems more likely that their arrival was a combination of invasions & migrations.
Archaeological finds of chariots maybe few for now, but that itself isn't enough to discredit the invasion. The fact that the Aryans are associated with horses & chariots is a flawed analogy because the Harappans were aware of horses. The Vedic people did not discriminate between the kind of equus animals used to draw chariots, & that they used other equus animals besides horses is consistent with archaeological findings as far as I know. As for wheels, the Harappans themselves were aware of them as known through their symbolism & the Vedic tribes knew of them as well. A lack of archaeological findings of wheels is discredited by the fact that the concept of the wheel dates back to the pre-Aryan period. Another important point to note is that at the moment our knowledge of both the Aryans & particularly the Harappans is severely lacking due to our failure at decrypting the Indus script. By the way, there is evidence of regular horses being used by Aryans, & the horse burial style is similar to that described in the Vedas. I will add some interesting information related to this topic & the overall subject of the Indo-Aryans towards the end.
By the way, excavation of some Indus Valley sites shows evidence of large scale massacres & killings. Many scholars have considered that itself to be proof of the Aryan invasion. Similarly, I have also read accounts that challenge the authenticity of the Vedas today, at this point we do not know how much of the Vedas were corrupted. Remember that the Vedas is to Aryans as the Pentateuch is to the Children of Israel, it isn't too far fetched to assume that both have been corrupted over generations. Sometimes I myself get the feeling that certain dates or stories presented in the Vedas seem extremely exaggerated, including the stories referring to the Gods aiding Aryan conquests. My advice would be to not consider the Vedas as authentic as the Quran. Another factor to take in to consideration is that, what reason do the Vedas have to lie about the conquest carried out by fair skinned people? If it had not taken place, why would the people of that time come up with such a story?
Speaking of cultural continuity, the Vedic Aryans adopted many of the customs & traditions of the Harappan people, & to some extent managed to corrupt their own cultures over time. A similar thing occurred when the Persians & Medians arrived to the Iranian plateau & were influenced by Semitic cultures. Remember, the Aryans were initially nomadic tribes, & even the Sanskrit language at that point was unwritten. Other civilizations such as the Greeks adopted & modified the scripts developed by others such as the Phoenicians. Sanskrit is the oldest surviving Indo-European language in existence, how do you explain its existence in the Sub-Continent knowing that the only other related language called Avestan was spoken in the Iranian plateau? Similarly, its other sister Indo-European languages were spoken in Europe, what were they doing there & how did Sanskrit arrive in the Sub-Continent if no ancient Indo-European people once came to the Sub-Continent? The fact is that all sister languages were originally sprouted from a group of related people, similar to case of Arabic, Hebrew, Phoenician, etc.
I have already mentioned the similarity between the Aryan & Greek Pantheon. The Persians & Medians themselves are historically known to have referred to the Aryans of the Indus. Alexander the Great or should I say the Hellenic people knew about them as well. The Sanskrit language & Aryan culture is Indo-European. One important point that I want to make here is that many people hate the Aryan invasion theory because of ideological reasons, they feel it causes divisions & is a remnant of British colonialism. I am strongly against that view, the truth will remain the truth regardless of how much someone wishes to deny it.
Let's move on to genetic evidence. As I recall the haplogroup R1a is prevalent in most Pakistani people, particularly in the northern regions. That same haplogroup & its branches are present in some regions of Eastern Europe, Central Asia, etc. In some ways, this proves their migration from Central Asia.
Map of Haplogroup R1a of Y-DNA
That is genetic evidence of the existence of the Indo-Aryan people. So far cultural, linguistic, historical, & genetic evidence point to their existence. Let me bring up the subject of race in this discussion. It is pointless to assume that the only difference between the Vedic people & the indigenous people is skin color. Race is not just about skin color, but takes in to consideration other phenotypes such as skull shape, body structure, etc. Race does exist, & that itself is evidence of the difference between the various ethnic groups in the Sub-Continent.
Finally, here is an article about unearthed Aryan cities that finally manages to change our perception of history. This new evidence points to the existence of the historical homeland of the Aryans called Andronovo & proves that the references present in the Vedas of the Aryan invasion were indeed accurate.
I have quoted some relevant portions of the article below.
Unearthed Aryan cities rewrite history
I think this should be more than enough evidence that a group of Indo-European tribes that referred to themselves as Aryans did indeed settle in the Indus, & they spoke their own Indo-European language called Sanskrit.
I never brought up the Europeans, but the fact remains that some Indo-European tribes in Andronovo migrated towards Europe as well.
Below is another link I just discovered. I didn't get time to go through it, but I will post it anyway.
Recent Archeological Finds Confirming Vedic History