If you have an itin# then you should have tax transcripts too. As long as you have tax transcripts & a "good job", then you would be eligible to apply for a loan. Getting approved for a loan though is a whole other matter. Approvals for traditional financing options these days are contingent on so many other factors besides verification of income. Other factors are assets, liabilities, employment etc.
As you may have discovered, simply having a good job is not enough to qualify for a loan. There are some lending sources that may not require tax transcripts but they will not be traditional lending options but rather more likely to be either portfolio lenders or hard money lenders. If you have any other questions and/or concerns or if I can be of any assistance, please feel free to contact me.