using System;

using System.Linq;

using System.Collections.Generic;

public class Program

{

    public static void Main()

    {

        var model = new Dictionary<string, Dictionary<string, Model>>

        {

            {

                "BaseKey1",

                new Dictionary<string, Model>

                {

                    {"SubKey1", new Model { Time = new DateTime(2020, 09, 15)}},

                    {"SubKey2", new Model { Time = new DateTime(2020, 12, 15) }}

                }

            },

​

            {

                "BaseKey2",

                new Dictionary<string, Model>

                {

                    {"SubKey1", new Model { Time = new DateTime(2020, 11, 15) }},

                }

            }

        };

​

        var result = model.Values.SelectMany(x => x).GroupBy(x => x.Key).ToDictionary(x => x.Key, x => x.Select(m => m.Value).MinBy(m => m.Time));

        result.Dump();

    }

}

​

public class Model

{

    public DateTime Time { get; set; }

    public override string ToString() => Time.ToString();

}

​

public static class EnumerableExtensions

{

    public static TSource MinBy<TSource, TKey>(

        this IEnumerable<TSource> source,

        Func<TSource, TKey> selector,

        IComparer<TKey> comparer = null)

    {

        if (source == null) throw new ArgumentNullException(nameof(source));

        if (selector == null) throw new ArgumentNullException(nameof(selector));

        comparer ??= Comparer<TKey>.Default;

​

        using (var sourceIterator = source.GetEnumerator())

        {

            if (!sourceIterator.MoveNext())

            {

                throw new InvalidOperationException("Sequence contains no elements");

            }

            var min = sourceIterator.Current;

            var minKey = selector(min);

            while (sourceIterator.MoveNext())

            {

                var candidate = sourceIterator.Current;

                var candidateProjected = selector(candidate);

                if (comparer.Compare(candidateProjected, minKey) < 0)

                {

                    min = candidate;

                    minKey = candidateProjected;

                }

            }

            return min;

        }

    }   

}