To answer clearly: under TRID, the soonest you can close after sending the Loan Estimate (LE) depends on timing requirements for disclosures and for signing documents, but the typical shortest practical window is about 7 business days from LE receipt to delivery of the Closing Disclosure (CD), plus the 3-business-day CD waiting period, before signing the loan documents. In many cases, lenders aim for a 7–10 day window, but TRID also requires the CD to be issued with at least 3 days before signing, and the CD must reflect the LE within a 10% variance (or trigger another 7-day wait if it does not). Some lenders and scenarios may extend this beyond the minimum, especially if additional documentation or underwriting conditions arise. For a concise outline:

• LE must be provided early in the process; the CD cannot be signed until at least 3 business days after the CD is mailed or delivered to the borrower.
• Closing cannot occur before the CD delivery and the 3-day waiting period are satisfied.
• The total minimum timeline from LE to closing commonly falls around 10–15 business days in straightforward cases, but not less than the 3-day CD wait plus any required verification and underwriting steps.
• If the Closing Disclosure amount changes beyond a 10% variance from the LE, a new CD and a new 3-day waiting period may be required, which can delay closing further.

If you want, I can pull the latest official CFPB TRID guidance and summarize the exact timing requirements for your jurisdiction and loan type.