The real interest comes from investors that wire the funds into your bank account. Otherwise it might mean interest in your specific market and not necessarily your company.
A good example of the above, is when you are getting inbound emails from associates or analysts at a Venture Capital firm. These folks are for the most part tasked by the partners to scout the space for data to form their investment thesis or because they are looking at investing in one of your competitors.
As you very well stated, the background of the team is critical. Like author Jim Collins states, a startup is ultimately a bus without direction. If you have the right people on the right seats of the bus it will eventually find the right direction towards success. With this in mind, by having this front covered you will be checking one of the critical boxes to get the investor excited.
The other critical component is the market in which you are executing as that will eventually determine the potential exit of the investor. You may have a great team but if the market is really small it may turn off some of these folks.
You may not have the tech ready, but it would be great if you could get some form of initial non-binding commitment from these potential customers (e.g. Letter of Intent) that you could later use to show your momentum to some of these investors as the conversations advance. Don't just walk away from them!
Like you cite, there are a lot of angels out there. Those are not the ones that call themselves "angel investors" on LinkedIn (these are from my experience the $2,000 ticket size types), but the senior executives at large corporations or entrepreneurs that had an exit with a previous venture that are looking to allocate between 5% - 8% of their portfolio to risky investments.
Please note it is not a matter of getting in front of the angels, it is all about knowing the strategy and the psychology required in order to enroll them with your future vision. Fundraising comes down to addressing concerns from the investor but it requires a masterful execution from A to Z.
In order to get things in motion with your financing round you will need one of the following things:
1) A lead investor
2) A syndicate
The first option is the challenging one. This lead investor will be establishing the terms of your round (e.g. valuation, term sheet, etc) where everyone else will be coming in.
Unfortunately not everyone leads and investors are like a sheep. They always follow other investors but not all of them take the charge to put the price and invest in a company. For that reason during the fundraising process try to avoid meeting with followers and invest your time with potential lead investors.
A good strategy to secure a lead investor is to incentivize your potential good candidate with an advisory role so that they get familiar with you and your team and the direction of the business. This way leading your round will come from them automatically.
The second option is putting together a syndicate. You would just put a valuation that is attractive and start generating momentum with a closing date to get people excited to join.
At the end of the day fundraising will depend on the level of FOMO (aka fear of missing out) that investors feel. No one wants to invest in a train that never leaves the station. However, if they feel they might miss the train or the ticket might be more expensive they would do whatever it takes to jump in.
With that being said, to build such urgency shoot for a closing date once you either have the syndicate or the lead in place but don't stick to it. It also helps to align product launches and media mentions praising your business during the fundraising period.
You will be using the updates above for the follow ups every two weeks with the investor (e.g. press mention, product launch, new hire, intro to an interesting entrepreneur that may fir the investment thesis of the investor, etc).
Also never mention that you are fundraising (good job btw on posting this as anonymous!) as the clock starts to tick the minute you do so. For example, if you tell someone that you are fundraising and you go back two months later he/she will think that everyone else rejected you.
With the above in mind, and like the saying goes, you ask for money and you will get advice. You ask for advice and you will get money twice. For that reason start building relationships with investors from day 1.
The best way to get in front of investors is by securing a great introduction. These introductions are really important as investors use the source that is introducing you to vet you. The angel networks are not gated, you just need the right person to invite you to the party...
With this in mind, try to get an intro from an entrepreneur that has made returns to that investor. This info is public on the internet and entrepreneurs are all about paying it forward. Just reach out to connect, tell the portfolio founder your story, and politely ask for an introduction to that specific investor that you'd like to meet.
Hope this helps :)