I will be sending out a preliminary lien notice but want to know how soon after I can submit the lien?
You really should retain a construction attorney to review and evaluate your legal position based on the contract and pertinent documents. The right to be entitled to file a mechanic's lien is set out in Texas Property Code Chapter 53, and you really need to make sure that if you file a lien, you have properly and appropriately done so.
Filing an invalid lien could subject you to liability under the Texas Fraudulent Lien Act, and you could be liable for statutory damages of $10,000, or actual damages, whichever is greater, plus attorney's fees. Facing such a claim would add insult to injury.
You do not provide enough information for a construction attorney to evaluate your legal situation. The legal requirements are different depending on whether you contracted with the owner, or the original contractor, or a subcontractor, and whether the project is commercial or residential.
Good luck.