Error when trying to install TinyTeX using tinytex R package "cannot contact mirror.ctan.org, returning a backbone server!"

Question

I am trying to use RMarkdown to knit my report to a pdf. I am on my work computer (without administrative privileges and behind a firewall), and chose TinyTeX as a LaTeX distribution because I was hoping it would still work without having to involve the IT department (at my place of work it takes ages to get elevated privileges). I had no problems installing the tinytex R package, but I run into errors when using the package to install TinyTeX. The code with errors is below:

>tinytex::install_tinytex()
trying URL 'http://mirror.ctan.org/systems/texlive/tlnet/install-tl.zip'
trying URL 'http://mirror.ctan.org/systems/texlive/tlnet/install-tl.zip'
Content type 'application/zip' length 22541272 bytes (21.5 MB)
downloaded 21.5 MB

trying URL 'https://yihui.org/gh/tinytex/tools/pkgs-custom.txt'
trying URL 'https://yihui.org/gh/tinytex/tools/pkgs-custom.txt'
Content type 'text/plain; charset=utf-8' length 551 bytes
downloaded 551 bytes

trying URL 'https://yihui.org/gh/tinytex/tools/tinytex.profile'
trying URL 'https://yihui.org/gh/tinytex/tools/tinytex.profile'
Content type 'text/plain; charset=utf-8' length 295 bytes
downloaded 295 bytes

Then at this point I get a dialog box that pops up and states: "Next you may see two error dialog boxes about the missing luatex.dll, and an error message like "Use of uninitialized value in bitwise or (|)..." in the end. These messages can be ignored." When I click 'Okay', I don't see any other dialog boxes but I get the following code:

Starting to install TinyTeX to C:\Users\*****\AppData\Roaming/TinyTeX. It will take a few minutes.
Automated TeX Live installation using profile: ../tinytex.profile
cannot contact mirror.ctan.org, returning a backbone server!
Loading http://www.ctan.org/tex-archive/systems/texlive/tlnet/tlpkg/texlive.tlpdb

C:\Users\*****\AppData\Local\Temp\RtmpgHbZh0\install-tl-20200214\install-tl: TLPDB::from_file could not initialize from: http://www.ctan.org/tex-archive/systems/texlive/tlnet/tlpkg/texlive.tlpdb
C:\Users\*****\AppData\Local\Temp\RtmpgHbZh0\install-tl-20200214\install-tl: Maybe the repository setting should be changed.
C:\Users\*****\AppData\Local\Temp\RtmpgHbZh0\install-tl-20200214\install-tl: More info: https://tug.org/texlive/acquire.html
TinyTeX installed to C:\Users\*****\AppData\Roaming/TinyTeX
Please quit and reopen your R session and IDE (if you are using one, such as RStudio or Emacs) and check if tinytex:::is_tinytex() is TRUE.
Warning messages:
1: In download.file(url, output, ..., method = method) :
  URL 'http://mirror.ctan.org/systems/texlive/tlnet/install-tl.zip': status was 'Couldn't connect to server'
2: In download.file(url, output, ..., method = method) :
  URL 'https://yihui.org/gh/tinytex/tools/pkgs-custom.txt': status was 'Couldn't connect to server'
3: In download.file(url, output, ..., method = method) :
  URL 'https://yihui.org/gh/tinytex/tools/tinytex.profile': status was 'Couldn't connect to server'
4: In file.remove("TinyTeX/install-tl.log") :
  cannot remove file 'TinyTeX/install-tl.log', reason 'No such file or directory'

After this, I try tinytex:::is_tinytex() and I get FALSE.

I am using R version 3.6.2, RStudio version 1.2.1335 and I'm on a Windows 10 x64.

I'm not familiar enough with R, RMarkdown or TinyTeX to understand what is going wrong and how to fix it. Perhaps it is because of no admin rights or the firewall...Any help is appreciated!