The regs basically say that you need 1500 hours of total time to earn your ATP and be eligible to upgrade to Captain (PIC). Some airlines determine their own eligibility requirements above what the regs require. (4) States the min of 250 PIC, but can be as SIC acting as PIC as well as the XC and Night time.

61.159 Aeronautical experience: Airplane category rating.
(a) Except as provided in paragraphs (b), (c), and (d) of this section, a person who is applying for an airline transport pilot certificate with an airplane category and class rating must have at least 1,500 hours of total time as a pilot that includes at least:
(1) 500 hours of cross-country flight time.
(2) 100 hours of night flight time.
(3) 75 hours of instrument flight time, in actual or simulated instrument conditions, subject to the following:
(i) Except as provided in paragraph (a)(3)(ii) of this section, an applicant may not receive credit for more than a total of 25 hours of simulated instrument time in a flight simulator or flight training device.
(ii) A maximum of 50 hours of training in a flight simulator or flight training device may be credited toward the instrument flight time requirements of paragraph (a)(3) of this section if the training was accomplished in a course conducted by a training center certificated under part 142 of this chapter.
(iii) Training in a flight simulator or flight training device must be accomplished in a flight simulator or flight training device, representing an airplane.
(4) 250 hours of flight time in an airplane as a pilot in command, or as second in command performing the duties of pilot in command while under the supervision of a pilot in command, or any combination thereof, which includes at least—
(i) 100 hours of cross-country flight time; and
(ii) 25 hours of night flight time.

So you should be able to easily meet ATP mins while SIC for any airline.