Final answer:
The factor that promotes the binding of the first tRNA to mRNA already bound to the 30S subunit is IF-3 (Initiation Factor-3). IF-3 helps prevent premature binding of the large ribosomal subunit and promotes proper positioning of the small ribosomal subunit on the mRNA.
Step-by-step explanation:
The factor that promotes the binding of the first tRNA to mRNA already bound to the 30S subunit in the initiation complex is IF-3 (Initiation Factor-3). IF-3 helps to prevent premature binding of the large ribosomal subunit and promotes the proper positioning of the small ribosomal subunit on the mRNA.