I am an intermediate excel user struggling to create a specific chart for an internship project. I have spent a lot of time trying to figure it out and have searched the web extensively.
Below is an example chart with example data:
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What you describe is a Marimekko chart, or variable width column chart. They can be created in Excel using the Area chart and a well-organised data layout.
Excel MVP and charting guru Jon Peltier has a step by step tutorial here:
Edit: The screenshot shows your data, the data layout required (truncated) and the final chart.
Create a data table as in columns F to H in the screenshot, insert an Area chart for that data, with column F as the X axis. Change the X axis from category to time axis. Use the label helper table to add a data series, send it to the secondary axis, make it a line chart, use a date axis. Use the free XY Chart Labeler add-in to place the labels below the data markers of the line. Hide the line, data markers and unwanted axes lines and labels.