If you have checked luggage, there’s no question about it, you will need to go through passport control and you will need a visa for this. End of story.
If for any other reason you have to go through passport control, like for instance if you can’t do mobile check-in and need to get to a check-in desk, same thing.
If you don’t, you could in theory make that connection without a visa. Except for a few cases of specific nationalities at specific airports which need an Airport Transit Visa even in this situation, Schengen countries do not care, as long as you have a confirmed onward flight quite soon (the rules as published on Timatic for the Netherlands say “on the same plane or on the first available connection”) and you stay airside (in the “international area”, which means you don’t have to got through passport control, which implies you can’t claim and recheck luggage). If you managed to get to Amsterdam, nobody would prevent you from making that connection.
The trouble is that airlines have a duty to the destination country to only carry passengers which meet the rules. If a passenger gets to passport control without a visa when they need one, the airline will receive a hefty fine and will have to carry the passenger back.
If the airline sold you a connecting flight, they know you meet the conditions. If ever there’s a problem with the connection, they have to take care of you (rebook you and so on), so you still meet the conditions.
But if you book two separate tickets, they have no way of being sure you really have that onward flight. They probably can’t check the status of your booking (and don’t want to), or even if it’s a real ticket! Most importantly, if there’s any sort of disruption which means you miss your ongoing flight, the gates of hell open for you and for them: the other airline will consider you a no-show, cancel your ticket, you’re stuck having to buy a new ticket at last minute prices, on some routes at certain times there may not be any availability for days, you have a strong chance of either being stuck at the airport for a while or come knocking at passport control, they get fined, they have to carry you back, they will try to charge you for that fine (yes, that’s in the terms and conditions you agreed to)…
They don’t want to deal with that. They sold you a ticket to go to Amsterdam. Can you enter the Netherlands? Please board. You can’t because you don’t have a visa? Sorry, can’t let you board.
Some agents will be convinced by a Timaric lookup and whatever proof you have of your onward flight. Most won’t. The rules are already complex enough when dealing with the connections they sell, they don’t want to take any risk for the connections they don’t.
When they sell a connection, they factor in the risks associated (having to rebook you, paying for hotels and meals if necessary, etc.). If you’re not willing to pay the price for those assurances, why should they?
Some airlines may accept to do that. Contact the first airline and get a guarantee in writing that they will let you board in those conditions (fat chance of that happening!). If they do, bring a copy of that to the airport, and good luck. But most probably they won’t guarantee anything, and then at the airport you have a very small chance they will let you board.
Bottom line: rebook as a single ticket or find a different itinerary where you can enter the connecting country.