I have three groups (with multiple replicates each) from 3 different locations. How can I obtain the DEG between the three groups since I have no control to compare to? I would like to obtain a list of the DEG across samples, and then run pairwise tests ANOVA + posthoc of specific genes between the three regions.

Would this be the way? Is there a better of more efficient way of doing this?

 dds <- DESeqDataSetFromMatrix(countData = cts,
                                  colData = coldata,
                                  design = ~ region)

Then

# ANOVA
anova <- aov(df_genes$Value ~ df_genes$Region)
summary(anova)

# Tukey test
tuckey.test<- TukeyHSD(anova)
tuckey.test

See the LRT section of the DESeq2 vignette. We do not have post-hoc pair-wise comparisons automatically enabled, but you could perform the pair-wise comparisons yourself with contrast and setting test="Wald" and use a two-stage framework such as stageR (another Bioc package, see their vignette for details).