Galaxy questions are better answered on the Galaxy site. Having said that, there's a tool under "Get Data" on the left called "EBI SRA". That can be used to load files from ENA, which largely has the same files as SRA, into Galaxy without using your bandwidth (at least it shouldn't). I imagine that this is throttled, so it still may take a while to get things.

Here's an example of how to analyze RNA-seq data from SRA (without using Galaxy and without downloading the data!). First you need four things.

1. Obtain an SRR accession of interest, i.e. a set of RNA-seq runs from the SRA database at NCBI. Try browsing the SRA website, then use the "Send to" pulldown and send the results to the Run Selector to help choose SRR accessions from your favorite data set(s).
2. Obtain HISAT, a really fast aligner.
3. The HISAT installation instructions tell you that to use SRA data directly you also need to install NCBI-NGS toolkit, and you should follow the installation details given in the HISAT manual.
4. Obtain a reference genome (e.g. I use chromosome 20 because it's conveniently small, in this case below from Ensembl, but you can try it from NCBI or UCSC as well).

Prepare your reference genome:

$ hisat-build Homo_sapiens.GRCh38.dna_rm.chromosome.20.fa Homo_sapiens.GRCh38.dna_rm.chromosome.20.fa_hisat

Then you can perform alignment and generate a SAM file, here analyzing data from the well-studied cell line GM12878:

$ hisat -x ../reference/Homo_sapiens.GRCh38.dna_rm.chromosome.20.fa_hisat --sra-acc SRR038448 -S myAlignment1.hisat.SRR038448.GRCh38.chr20.sam

The -x argument points to your reference genome, the --sra-acc argument is to specify the SRR run accession, and -S is the name of your SAM file. Typical next steps might be to use samtools to compress your file to BAM, sort, and index; then use stringtie to assemble gene models and quantify expression; and perhaps IGV to visualize your results.

This example is from an RNA-seq lecture in the ongoing NCBI NOW workshop (Biostar tags linked here). Good luck!