The significance of random mutations in the Origins debate

The very first reference itself answers your question. It reported:
“Because clinical resistance typically requires three to five independent mutations the data imply that in the absence of efficient LexA cleavage, E. coli would evolve clinical resistance at least 10^6 -fold slower.”

Compared to traditional mutation models, Stress-induced mutagenesis (SIM) models better fixes the problem of evolving complex adaptations. (Complex adaptations refers to adaptations that depend on the fixation of multiple, specific mutations, where intermediate stages of evolution seemingly provide little or no benefit. Complex adaptations are pervasive in molecular systems).

For example, a 2014 theoretical study reported: “Our results suggest that SIM can help resolve the problem of fitness valley crossing by reducing the time required for a population to shift an adaptive peak.”
The paper added:
“Our results show that SIM increases the rate of complex adaptation…”
(https://doi.org/10.1098/rspb.2014.1025)

■ An important thing to consider along with this is that living systems are equipped with molecular chaperones. These chaperones are able to alleviate or buffer the deleterious effects of mutations and stabilize proteins. This built-in feature promotes evolution.
Conversely, the first hypothetical self-replicating system would obviously lack such molecular chaperones to buffer against deleterious mutations.

■ Comparing evolution driven by plasticity and traditional mechanism, a 2010 paper stated:

“In contrast to the rapid response produced by plasticity, if the production of newly favored phenotypes requires new mutations, the waiting time for such mutations can be prohibitively long and the probability of subsequent loss through drift can be high”
(https://doi.org/10.1016/j.tree.2010.05.006)