First, if the other company has a lower serial number than yours, then they filed their application first. The fact that it did not appear in the USPTO online system does not mean that it was not already on file since there is a delay before newly filed applications reach the system.
However, who filed first is not the key issue since the US is a first to use, not a first to file, system. Thus, if your date of first use (assuming you did not file an intent-to-use application) is earlier than the other company's date of first use, if any yet, then you would have priority over the other company.
Not mentioned by you is whether or not the other company has filed for the same goods and/or services as you have. If not and the goods/services are unrelated, it is possible that mark could be registered to both of you.
Answered on Apr 30th, 2014 at 10:29 AM