How do I perform Non Linear Least Squares in R with a pre determined lag structure - r

Question

Suppose I want to estimate the parameters of the following model:
$y_t = beta0 (sum_{i=1}^p w(delta;i) x_{t-i})$.
Latex version of the equation: https://i.stack.imgur.com/POOlD.png
Where y_t and x_{t-i} are known data points, wdelta follows an exponential Almon lag structure with two parameters delta1 and delta2(see image). And beta0 is the common parameter.
Generating some data for x and y
y <- seq(1:10)
x <- rnorm(10,2,5)
The literature suggests estimating the model parameters using NLS and the Gaussian Newton Method. R does have a function gaussNewton however I am not sure how to use this. How do I approach the estimation of the parameters beta0,delta1 and delta2?
Wikipedia suggest: https://en.wikipedia.org/wiki/Non-linear_least_squares, however I feel like this is not appropriate in this case.
The nls function in R is unable to deal with predefined lag structures so this is not an option either. Maybe I could write out the function in the form of the sum of squared residuals and use the optim function? Another option could be to use the nlm function.
nonls <- function(delta1,delta2,i,p) {
z <- exp(delta1 * i + delta2 *i)
wdelta[i] <- exp(delta1 * i + delta2 *i)/sum(z[1:i])
ssr <- (y[i]- (beta0 * wdelta[i] * x[i:p]))^2
}
optim(ssr)
I look forward to your suggestions.