Quick replace of NA - an error or warning

I have a big data.frame called "mat" of 49952 obs. of 7597 variables and I'm trying to replace NAs with zeros. Here is and example how my data.frame looks like:

    A   B   C   E   F   D   Q   Z   . . .
1   1   1   0   NA  NA  0   NA  NA
2   0   0   1   NA  NA  0   NA  NA
3   0   0   0   NA  NA  1   NA  NA
4   NA  NA  NA  NA  NA  NA  NA  NA
5   0   1   0   1   NA  0   NA  NA 
6   1   1   1   0   NA  0   NA  NA
7   0   0   1   0   NA  1   NA  NA 
.
.
.

I need realy fast tool to replace them. The result should look like:

    A   B   C   E   F   D   Q   Z   . . .
1   1   1   0   0   0   0   0   0
2   0   0   1   0   0   0   0   0 
3   0   0   0   0   0   1   0   0
4   0   0   0   0   0   0   0   0
5   0   1   0   1   0   0   0   0 
6   1   1   1   0   0   0   0   0
7   0   0   1   0   0   1   0   0 
.
.
.

I already tried lapply(mat, function(x){replace(x, is.na(x),0)}) - didn't work - mat[is.na(mat)] <- 0 - error and and maybe too slow - and also link - didn't work too.

@Sotos already advised me plyr::rbind.fill(lapply(L, as.data.frame)) but it didn't work, because it makes data.frame of 379485344 observations and 1 variable (which is 49952x7597) so I have to also trafnsform it back. Is there any better way to do this?

The real structure of my data.frame:

> str(mat)
'data.frame':   49952 obs. of  7597 variables:
 $ 6794602   : num  1 NA NA NA NA 0 0 0 0 0 ...
 $ 1008667   : num  NA 1 0 NA NA 0 0 0 0 0 ...
 $ 8009082   : num  NA 0 1 NA NA NA NA NA NA NA ...
 $ 6740421   : num  NA NA NA 1 NA 0 0 0 0 0 ...
 $ 6777805   : num  NA NA NA NA 1 NA NA NA NA NA ...
 $ 1001682   : num  NA NA NA NA NA 0 0 0 0 0 ...
 $ 1001990   : num  NA NA NA NA NA 0 0 0 0 0 ...
 $ 1002541   : num  NA NA NA NA NA 0 0 0 0 0 ...
 $ 1002790   : num  NA NA NA NA NA 0 0 0 0 0 ...

Note:

when I tried mat[is.na(mat)] <- 0 there was a warning:

> mat[is.na(mat)] <- 0
Warning messages:
1: In `[<-.factor`(`*tmp*`, thisvar, value = 0) :
  invalid factor level, NA generated
2: In `[<-.factor`(`*tmp*`, thisvar, value = 0) :
  invalid factor level, NA generated
> nlevels(mat)
[1] 0

Data.frame mat after using mat[is.na(mat)] <- 0:

> str(mat)
'data.frame':   49952 obs. of  7597 variables:
 $ 6794602   : num  1 0 0 0 0 0 0 0 0 0 ...
 $ 1008667   : num  0 1 0 0 0 0 0 0 0 0 ...
 $ 8009082   : num  0 0 1 0 0 0 0 0 0 0 ...
 $ 6740421   : num  0 0 0 1 0 0 0 0 0 0 ...
 $ 6777805   : num  0 0 0 0 1 0 0 0 0 0 ...
 $ 1001682   : num  0 0 0 0 0 0 0 0 0 0 ...
 $ 1001990   : num  0 0 0 0 0 0 0 0 0 0 ...
 $ 1002541   : num  0 0 0 0 0 0 0 0 0 0 ...
 $ 1002790   : num  0 0 0 0 0 0 0 0 0 0 ...

So the questions are:

1. Is there any other fast way to replace the NA?
2. Is the warning big deal? Because data after using mat[is.na(mat)] <- 0 looks like what I want, but there are too many values, so I can't check if they are all right.