Not so fast people-----
One of the requirements for the ATP is that you hold a commercial license:
FAR 61.153--Eligibility for an ATP
Sec. 61.153
Eligibility requirements: General.
To be eligible for an airline transport pilot certificate, a person must:
(a) Be at least 23 years of age;
(b) Be able to read, speak, write, and understand the English language. If the applicant is unable to meet one of these requirements due to medical reasons, then the Administrator may place such operating limitations on that applicant's pilot certificate as are necessary for the safe operation of the aircraft;
(c) Be of good moral character;
(d) Meet at least one of the following requirements:
(1) Hold at least a commercial pilot certificate and an instrument rating;
(2) Meet the military experience requirements under Sec. 61.73 of this part to qualify for a commercial pilot certificate, and an instrument rating if the person is a rated military pilot or former rated military pilot of an Armed Force of the United States; or
(3) Hold either a foreign airline transport pilot or foreign commercial pilot license and an instrument rating, without limitations issued by a contracting State to the Convention on International Civil Aviation.
(e) Meet the aeronautical experience requirements of this subpart that apply to the aircraft category and class rating sought before applying for the practical test;
(f) Pass a knowledge test on the aeronautical knowledge areas of Sec. 61.155(c) of this part that apply to the aircraft category and class rating sought;
(g) Pass the practical test on the areas of operation listed in Sec. 61.157(e) of this part that apply to the aircraft category and class rating sought; and
(h) Comply with the sections of this part that apply to the aircraft category and class rating sought.
You can use your prior hours but are not eligible for the license purely based upon your non-US military experience.
One of the requirements for a commercial license is----you guessed it---a private license.
It has been a while since I was in full time instruction---so I am open to being corrected, however, the way I read the FAR's, You will need to do ALL of them. Long gone are the days when you could go right to commercial.