Can you fly from Zagreb to the US without quarantining?

According to IATA (-> USA), one doesn't have to quarantine if arriving from Croatia. So all you have to do is ensure that you fly to the US via some other country. Current options are Serbia and Turkey - both have a direct flight to the US and both don't require you to quarantine on arrival.

3. Passengers who have been in Austria, Belgium, Brazil, China (People's Rep.), Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Iran, Ireland (Rep.), Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland or United Kingdom (excluding overseas territories outside of Europe) in the past 14 days but are exempt from the restriction to enter the USA, must self-quarantine for 14 days once they reach their final destination.

Full IATA information (note that if the passenger does a stopover and even just transit in some countries such as France, they won't even be allowed to enter the US (unless one is included in one of the exceptions, such as being a US citizen or LPR, in which one might have to self-quarantine):

United States (Published 31.07.2020)

1. Passengers who have transited or have been in Austria, Belgium, Brazil, China (People's Rep.), Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Iran, Ireland (Rep.), Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland or in the United Kingdom (excluding overseas territories outside of Europe), in the past 14 days are not allowed to enter and transit.

   This does not apply to:

• nationals and permanent residents of the USA;
• spouses of nationals and of permanent residents of the USA;
• parents/legal guardians of an unmarried and younger than 21 years national or permanent resident of the USA;
• the unmarried and younger than 21 years brother or sister of a national or permanent resident of the USA, who is unmarried and younger than 21 years;
• the child/foster child/ward of a national or permanent resident of the USA;
• passengers with the following visas: A-1, A-2, C-1, C-1/D, C-2, C-3, CR-1, CR-2, D, E-1 (as an employee of TECRO or TECO or the employee's immediate family members), G-1, G-2, G-3, G-4, IR-1, IR-4, IH-4, NATO-1 through NATO-4, or NATO-6 visa;
• members of the U.S. Armed Forces, spouses, and children of members of the U.S. Armed Forces;
• passengers with evidence of traveling at the invitation of the USA government for a purpose related to the containment/mitigation of the Coronavirus (COVID-19);
• passengers with documents issued by the U.S. Department of Homeland Security, U.S. Customs and Border Protection, or U.S. Department of State indicating that the passenger is exempt from the restriction;
• B1 crew crewmembers that are engaged in lightering, Outer Continental Shelf (OCS) activity, wind farm activity, private air/sea crew and other similar crewmember actives;
• students with an F-1 or M-1 visa and their F-2 and M-2 dependents, if they arrive from or have been in Ireland (Rep.), United Kingdom or Schengen Member States in the past 14 days.

2. Passengers who have been in one of the countries listed in bullet number 1 in the past 14 days but are exempt from the restriction to enter the USA, must arrive at one of the following airports: Atlanta (ATL), Boston (BOS), Chicago (ORD), Dallas, (DFW), Detroit (DTW), Ft. Lauderdale (FLL), Honolulu (HNL), Houston (IAH), Los Angeles (LAX), Miami (MIA), New York (JFK or EWR), San Francisco (SFO), Seattle (SEA) and Washington (IAD).
3. Passengers who have been in Austria, Belgium, Brazil, China (People's Rep.), Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Iran, Ireland (Rep.), Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland or United Kingdom (excluding overseas territories outside of Europe) in the past 14 days but are exempt from the restriction to enter the USA, must self-quarantine for 14 days once they reach their final destination.
4. Passengers arriving in Massachusetts must complete the "Massachusetts Travel Form" at https://www.mass.gov/forms/massachusetts-travel-form . They are subject to quarantine for 14 days.
5. Passports issued to nationals of Belarus which have expired between 30 April 2020 and 31 July 2020, are considered valid with an extension of 3 months.