R, 1042 bytes

The credit for this answer should go to digEmAll, who did 499(!) bytes better than my version (left below). Most characters are printed by using the octal representation, e.g. cat('\041') prints character number 41 in octal, or 33 in decimal, i.e. !. There are a few additional tricks, explained in my original answer below.

cat('','')
cat('\041')
cat('\042')
cat('\043')
cat('\044')
cat('\045')
cat('\046')
cat("\047")
`?`=cat;?'\050'
`?`=cat;?'\051'
cat('\052')
cat('\053')
cat('\054')
cat('\055')
cat('\056')
cat('\057')
cat(+F)
cat(+T)
cat(1+1)
cat(2+1)
cat(3+1)
cat(4+1)
cat(5+1)
cat(6+1)
cat(7+1)
cat(8+1)
cat('\072')
cat('\073')
cat('\074')
cat('\075')
cat('\076')
cat('\077')
cat('\100')
cat('\101')
cat('\102')
cat('\103')
cat('\104')
cat('\105')
cat('\106')
cat('\107')
cat('\110')
cat('\111')
cat('\112')
cat('\113')
cat('\114')
cat('\115')
cat('\116')
cat('\117')
cat('\120')
cat('\121')
cat('\122')
cat('\123')
cat('\124')
cat('\125')
cat('\126')
cat('\127')
cat('\130')
cat('\131')
cat('\132')
cat('\133')
cat(intToUtf8(92))
cat('\135')
cat('\136')
cat('\137')
cat('\140')
`c\141t`('\141')
cat('\142')
`\143at`('\143')
cat('\144')
cat('\145')
cat('\146')
cat('\147')
cat('\150')
cat('\151')
cat('\152')
cat('\153')
cat('\154')
cat('\155')
cat('\156')
cat('\157')
cat('\160')
cat('\161')
cat('\162')
cat('\163')
`ca\164`('\164')
cat('\165')
cat('\166')
cat('\167')
cat('\170')
cat('\171')
cat('\172')
cat('\173')
cat('\174')
cat('\175')
cat('\176')

Try it online!

R, 1040 bytes

-2 bytes by using as.name.

The credit for this answer should go to digEmAll, who did 499(!) bytes better than my version (left below). Most characters are printed by using the octal representation, e.g. cat('\041') prints character number 41 in octal, or 33 in decimal, i.e. !. There are a couple of minor additional tricks, explained in more detail in my original answer below. For the characters ct, use as.name instead of cat; for the characters () redefine the function ? which has a special syntax and doesn't need brackets.

The solution for a is

`c\141t`('\141')

since c\141t in backticks is interpreted as cat.

The other notable exception is the character \, for which we have to use the more standard cat(intToUtf8(92)).

cat('','')
cat('\041')
cat('\042')
cat('\043')
cat('\044')
cat('\045')
cat('\046')
cat("\047")
`?`=cat;?'\050'
`?`=cat;?'\051'
cat('\052')
cat('\053')
cat('\054')
cat('\055')
cat('\056')
cat('\057')
cat(+F)
cat(+T)
cat(1+1)
cat(2+1)
cat(3+1)
cat(4+1)
cat(5+1)
cat(6+1)
cat(7+1)
cat(8+1)
cat('\072')
cat('\073')
cat('\074')
cat('\075')
cat('\076')
cat('\077')
cat('\100')
cat('\101')
cat('\102')
cat('\103')
cat('\104')
cat('\105')
cat('\106')
cat('\107')
cat('\110')
cat('\111')
cat('\112')
cat('\113')
cat('\114')
cat('\115')
cat('\116')
cat('\117')
cat('\120')
cat('\121')
cat('\122')
cat('\123')
cat('\124')
cat('\125')
cat('\126')
cat('\127')
cat('\130')
cat('\131')
cat('\132')
cat('\133')
cat(intToUtf8(92))
cat('\135')
cat('\136')
cat('\137')
cat('\140')
`c\141t`('\141')
cat('\142')
as.name('\143')
cat('\144')
cat('\145')
cat('\146')
cat('\147')
cat('\150')
cat('\151')
cat('\152')
cat('\153')
cat('\154')
cat('\155')
cat('\156')
cat('\157')
cat('\160')
cat('\161')
cat('\162')
cat('\163')
as.name('\164')
cat('\165')
cat('\166')
cat('\167')
cat('\170')
cat('\171')
cat('\172')
cat('\173')
cat('\174')
cat('\175')
cat('\176')

Try it online!

Original version:

R, 1541 bytes

`?`=cat;`!`=intToUtf8;?!40

R, 1042 bytes

The credit for this answer should go to digEmAll, who did 499(!) bytes better than my version (left below). Most characters are printed by using the octal representation, e.g. cat('\041') prints character number 41 in octal, or 33 in decimal, i.e. !. There are a few additional tricks, explained in my original answer below.

cat('','')
cat('\041')
cat('\042')
cat('\043')
cat('\044')
cat('\045')
cat('\046')
cat("\047")
`?`=cat;?'\050'
`?`=cat;?'\051'
cat('\052')
cat('\053')
cat('\054')
cat('\055')
cat('\056')
cat('\057')
cat(+F)
cat(+T)
cat(1+1)
cat(2+1)
cat(3+1)
cat(4+1)
cat(5+1)
cat(6+1)
cat(7+1)
cat(8+1)
cat('\072')
cat('\073')
cat('\074')
cat('\075')
cat('\076')
cat('\077')
cat('\100')
cat('\101')
cat('\102')
cat('\103')
cat('\104')
cat('\105')
cat('\106')
cat('\107')
cat('\110')
cat('\111')
cat('\112')
cat('\113')
cat('\114')
cat('\115')
cat('\116')
cat('\117')
cat('\120')
cat('\121')
cat('\122')
cat('\123')
cat('\124')
cat('\125')
cat('\126')
cat('\127')
cat('\130')
cat('\131')
cat('\132')
cat('\133')
cat(intToUtf8(92))
cat('\135')
cat('\136')
cat('\137')
cat('\140')
`c\141t`('\141')
cat('\142')
`\143at`('\143')
cat('\144')
cat('\145')
cat('\146')
cat('\147')
cat('\150')
cat('\151')
cat('\152')
cat('\153')
cat('\154')
cat('\155')
cat('\156')
cat('\157')
cat('\160')
cat('\161')
cat('\162')
cat('\163')
`ca\164`('\164')
cat('\165')
cat('\166')
cat('\167')
cat('\170')
cat('\171')
cat('\172')
cat('\173')
cat('\174')
cat('\175')
cat('\176')

Try it online!

R, 1541 bytes

`?`=cat;`!`=intToUtf8;?!40

R, 1545 bytes

The function write is usually used to write to a file, but can be made to write to STDOUT: write(letters[1],'') works for a and c. Unfortunately, that still doesn't work for t. I almost gave up here.

R, 1541 bytes

The function write is usually used to write to a file, but can be made to write to STDOUT: write(letters[1],'') works for a and c. Unfortunately, that still doesn't work for t. I almost gave up here...