I don't know where to begin with this.
Finding a domain for a search engine is not easy you have to know if people would actually like the name. And it's not just people from one language and culture, you have to use a name that is good for multiple cultures and languages. Randomly picking a name that you personally think is good is not how to go about starting a competitive search engine.
A domain name does not matter, there are literally millions of options. Why can 2 students come up with Google.com as a brand name but a team of 50 computer scientists and 20 marketing people can't. They have already overcome the great fucking challenge of picking a domain name when they bought ahrefs.com - I don't know why picking a domain name gives you such doubt, I think they will manage it.
Lets be honest, bing.com is a bit shit. Camelcamelcamel.com is also something kind of crap. DuckDuckgo.com probably means fuck all in Indian.
This is a very strange point that you're so hung up on.
Google has the best search engine, there are other companies but they aren't as good when it comes to the results. It's not just getting 2-3 people in a room and giving them a week to put it together, its hundreds of people over years.
You clearly don't do SEO, you're on a forum with 1 million members who all game their algorithm and exploit it for our own gain.
Their results have also been getting progressively worse, I often use bing.com instead of Google.
Google also use standard sorting algorithms from data science, they don't actually invent things out of thin air. Writing sorting algorithms is not that difficult, Google do not have a monopoly on Algorithms.
Online Marketing is not the only marketing you have to do. Radio advertisements, Television advertisements, Billboards etc are all needed. They would need to hire a top tier marketing firm, not use an in-house marketing team.
Do you live in 1995? Radio adverts and television adverts for a search engine? I don't even know what to say.
Ahrefs marketing team are far superior to any agency I know. They have talent in depth and the budget to hire anyone they wish.
This again is a stupid argument. You have no idea how big Ahrefs actually are, their tool props up the vast majority of SEO agencies out there. To then claim they will have to hire agencies to do this is incredible. Ahrefs is a bootstrapped company, they have form and know what they are doing.
It's cheaper to use your own hardware than it is to use AWS.
It's actually not, that's why Lyft use AWS despite AWS costing $0.70 per job for them.
https://aws.amazon.com/solutions/case-studies/lyft/
Building a datacenter costs 10's of millions and as you say you would need to buy multiple DC's. You have hardware costs, engineers, security, power, cooling, building costs... It would also take years to set this up.
Or you can spin up AWS in 15 minutes and just piggyback on their system.
And for the third time, Ahrefs is the second biggest web crawler in the world. They ALREADY have the server power to launch a search engine.
Let me tell you a story.
My Grandfather smoked his whole life. I was about 10 years old when my mother said to him, 'If you ever want to see your grandchildren graduate, you have to stop immediately.'.
Tears welled up in his eyes when he realized what exactly was at stake. He gave it up immediately.
Three years later he died of lung cancer, it was really sad and destroyed me.
My mother said to me- 'Don't ever smoke. Please don't put your family through what your Grandfather put us through."
I agreed.
At 28, I have never touched a cigarette. I must say, I feel a very slight sense of regret for never having done it, because your post gave me cancer anyway.