Upvote:19
In general, as someone with dual citizenship you would be eligible to use the Visa Waiver Program (ie, ESTA) under either of your citizenships - it wouldn't matter if one of them isn't eligible for ESTA/VWP, as long as the one you apply for is.
However as you're likely aware, there are a few exceptions to this rule, and the following are not eligible to use the VWP program, even if they hold a citizen citizenship that would make them eligible :
Thus you are not eligible to use the Visa Waiver Program. If you attempt to apply for an ESTA to use this program, one of the question you will be asked is any other citizenships you hold, and your application will be automatically rejected due to your Syrian citizenship.
The only option is to apply for a US visa - most likely a B2 ("tourist") visa. Applying for a US visa involves paying a fee, making an appointment for and attending an interview at a US Consulate, and filling in a DS-160 form. Normally this is not an overly difficult process, however at the moment many US consulates are only providing limited services due to COVID-19.
The website for the US Consulate in Amsterdam states that they are currently providing "very limited non-immigrant visa services for students and certain petition-based workers who qualify for an exception to current travel restrictions.", however as the travel restrictions this refers to are due to be relaxed in November 2021 it's very likely that their rules will change in the near future - it may even be worth attempting to email them and ask if/when they expect this to occur.
If you are unable to obtain an appointment in Amsterdam you MAY be able to apply at the US Consulate in another country, but check the rules carefully as many are not accepting bookings from non-residents of the country they are in.
Unfortunately other than obtaining a visa you have no other options to travel to the US. The only legal way to bypass the Syrian exclusion from the VWP is to obtain a visa. Attempting to bypass it in other way (eg, not disclosing your Syrian citizenship) have to potential of ending very badly, up to and including you being banned from the US for life!