Plotting in ggplot2 with only an x axis requirement

Question

I have a dataframe, with NA's. State names are column headers, and dates are the row headers. How can I use ggplot() to plot the columns, with dates on the x axis, and some arbitrary scale on the y axis?

 Florida Iowa Pennsylvania Nevada Georgia South.Carolina Montana Maine  Arizona North.Carolina
January 2019        NA   NA           NA     NA      NA             NA      NA    NA       NA       46.33333
February 2019       NA   NA           NA     NA      NA             NA      NA    NA 40.25000       35.75000
March 2019          NA 48.2     49.66250  48.78      NA             NA      NA    NA       NA             NA
April 2019    44.00000 44.0     48.50000     NA      NA             NA      NA    NA       NA             NA
May 2019      48.36000   NA     47.33333     NA      NA             NA      NA    NA 40.66667             NA
June 2019     46.61429   NA     37.50000     NA      NA          34.25      NA  52.4       NA       46.60000

Is there a way to incorporate a 'predictive' connecting line between observations and NA's in the chart (by state) so that it may not be strictly linear through the unknown space?

I can get the x axis correct, but not the y or the plots.

ggplot(demplot, aes(x = seq.Date(from = as.Date('2019-01-01'), to = as.Date('2020-11-01'),by = "month"))