Is it possible to get my SPC laterally promoted to CPL now that SGT does not have to complete BLC before getting promoted?

No. Army policy hasn't changed (for RA and USAR) since the implementation in 2022 (AD 2021-17*, para 5c).

• In order to attend BLC, a SPC must be recommended for promotion.
• When the Solider graduates BLC, then they will be laterally appointed to CPL

As the Army has given prescriptive guidance, there aren't "alternative methods" that can be used to get around it (again, for RA and USAR Soldiers) - "The CPL rank will be worn only by Soldiers who are both recommended for promotion by a unit promotion board and graduates of the BLC, regardless of the grade of position to which they are assigned" (AD 2021-17, 5b(1)).
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* Army Directive 2021_17 _ https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN32643-ARMY_DIR_2021-17-000-WEB-1.pdf

I don't know if this is still current policy but found this:
"Published July 01, 2021
The Army on Thursday revamped how junior soldiers will move up to leadership positions, requiring all enlisted soldiers to first pin on the rank of corporal before they can become sergeants.

All soldiers with the rank of specialist who complete the Basic Leader Course, or BLC, and are recommended for advancement by a promotion board will be promoted laterally to corporal, according to new Army policy announced last month. BLC is a required Army school to transition troops from the junior ranks to noncommissioned officers."

Then this ALARACT: ALARACT 050/2021
DTG: R 071457Z JUN 21 SUBJ/ALARACT 050/2021 – LATERAL APPOINTMENT TO CORPORAL AND
ELIGIBILITY FOR BASIC LEADERS COURSE

Again I don't know if that changed. But that's what comes up when I search lateral promotion to CPL. That is from 2021 - but for awhile you had to be a BLC graduate and SPC P to get a lateral appointment to CPL approved.

A Lateral Promotion, specific to the unit, is merely a 4187 approved by the unit commander.