In some cases the answer is yes. For instance, as of 2020, there is a pathway for "SBIR Direct Phase II" awards for NIH (one of the grant giving agencies). According to the NIH SBIR FAQ page in 2020:
As part of the SBIR and STTR Reauthorization of 2011, NIH may ‘issue a Phase II award to a small business concern that did not receive a Phase I award for that research/research & development'. This 'phase flexibility' is called a ‘Direct-to-Phase II’ SBIR award. This permits small businesses to receive a Phase II award even if they have not previously received a Phase I award for the research/research and development of their technology. In order to be eligible for the SBIR Direct Phase II award, the small business must have performed the Phase I stage-type of research through other funding sources.
The Direct-to-Phase II authority is not available to the STTR program and not available for the CDC, FDA, and ACL SBIR programs.
The prior program had specific SBIR Direct-to-Phase II funding opportunity announcements (FOAs). The transition to FORMS-E allows NIH to track SBIR Direct-to-Phase II applications at the Application level, as there is a new check-box on the SBIR/STTR Information Form for Direct Phase II.
As a result of this, NIH does not need to issue separate SBIR Direct-to-Phase II FOAs as before, but can offer Direct-to-Phase II as an allowable Application Type on any SBIR FOA. SBIR Direct-to-Phase II application are 'New' submissions and are not Renewals.
Applicants are strongly advised to discuss this option with their Program Officer well in advance of any due date.